\input texinfo @c -*-texinfo-*-

@c %**start of header

@setfilename gnuplot.info

@settitle Gnuplot: An Interactive Plotting Program

@setchapternewpage odd

@c %**end of header

@c define the command and options indeces

@defindex cm

@defindex op

@defindex tm

@direntry

* GNUPLOT: (gnuplot). An Interactive Plotting Program

@end direntry

@ifnottex

@node Top, gnuplot, (dir), (dir)

@top Master Menu

@end ifnottex

@example

GNUPLOT

An Interactive Plotting Program

Thomas Williams & Colin Kelley

Version 3.7 organized by: David Denholm

Copyright (C) 1986 - 1993, 1998 Thomas Williams, Colin Kelley

Mailing list for comments: info-gnuplot@@dartmouth.edu

Mailing list for bug reports: bug-gnuplot@@dartmouth.edu

This manual was prepared by Dick Crawford

3 December 1998

Major contributors (alphabetic order):

@end example

@c ^ <h2> An Interactive Plotting Program </h2><p>

@c ^ <h2> Thomas Williams & Colin Kelley</h2><p>

@c ^ <h2> Version 3.7 organized by: David Denholm </h2><p>

@c ^ <h2>Major contributors (alphabetic order):</h2>

@itemize @bullet

@item

Hans-Bernhard Broeker

@item

John Campbell

@item

Robert Cunningham

@item

David Denholm

@item

Gershon Elber

@item

Roger Fearick

@item

Carsten Grammes

@item

Lucas Hart

@item

Lars Hecking

@item

Thomas Koenig

@item

David Kotz

@item

Ed Kubaitis

@item

Russell Lang

@item

Alexander Lehmann

@item

Alexander Mai

@item

Carsten Steger

@item

Tom Tkacik

@item

Jos Van der Woude

@item

James R. Van Zandt

@item

Alex Woo

@end itemize

@c ^<h2> Copyright (C) 1986 - 1993, 1998 Thomas Williams, Colin Kelley<p>

@c ^ Mailing list for comments: info-gnuplot@@dartmouth.edu <p>

@c ^ Mailing list for bug reports: bug-gnuplot@@dartmouth.edu<p>

@c ^</h2><p>

@c ^<h3> This manual was prepared by Dick Crawford</h3><p>

@c ^<h3> 3 December 1998</h3><p>

@c ^<hr>

@menu

* gnuplot::

* Commands::

* Graphical_User_Interfaces::

* Bugs::

* Concept_Index::

* Command_Index::

* Options_Index::

* Function_Index::

* Terminal_Index::

@end menu

@node gnuplot, Commands, Top, Top

@chapter gnuplot

@menu

* Copyright::

* Introduction::

* Seeking-assistance::

* What's_New_in_version_3.7::

* bind::

* Batch/Interactive_Operation::

* Command-line-editing::

* Comments::

* Coordinates::

* Environment::

* Expressions::

* Glossary::

* Plotting::

* Start-up::

* Substitution::

* Syntax::

* Time/Date_data::

@end menu

@node Copyright, Introduction, gnuplot, gnuplot

@section Copyright

@cindex copyright

@cindex license

@example

Copyright (C) 1986 - 1993, 1998 Thomas Williams, Colin Kelley

@end example

Permission to use, copy, and distribute this software and its

documentation for any purpose with or without fee is hereby granted,

provided that the above copyright notice appear in all copies and

that both that copyright notice and this permission notice appear

in supporting documentation.

Permission to modify the software is granted, but not the right to

distribute the complete modified source code. Modifications are to

be distributed as patches to the released version. Permission to

distribute binaries produced by compiling modified sources is granted,

provided you

@example

1. distribute the corresponding source modifications from the

released version in the form of a patch file along with the binaries,

2. add special version identification to distinguish your version

in addition to the base release version number,

3. provide your name and address as the primary contact for the

support of your modified version, and

4. retain our contact information in regard to use of the base

software.

@end example

Permission to distribute the released version of the source code along

with corresponding source modifications in the form of a patch file is

granted with same provisions 2 through 4 for binary distributions.

This software is provided "as is" without express or implied warranty

to the extent permitted by applicable law.

@example

AUTHORS

@end example

@example

Original Software:

Thomas Williams, Colin Kelley.

@end example

@example

Gnuplot 2.0 additions:

Russell Lang, Dave Kotz, John Campbell.

@end example

@example

Gnuplot 3.0 additions:

Gershon Elber and many others.

@end example

@node Introduction, Seeking-assistance, Copyright, gnuplot

@section Introduction

@cindex introduction

@c ?

`gnuplot` is a command-driven interactive function and data plotting program.

It is case sensitive (commands and function names written in lowercase are

not the same as those written in CAPS). All command names may be abbreviated

as long as the abbreviation is not ambiguous. Any number of commands may

appear on a line (with the exception that `load` or @ref{call} must be the final

command), separated by semicolons (;). Strings are indicated with quotes.

They may be either single or double quotation marks, e.g.,

@example

load "filename"

cd 'dir'

@end example

although there are some subtle differences (see `syntax` for more details).

Any command-line arguments are assumed to be names of files containing

`gnuplot` commands, with the exception of standard X11 arguments, which are

processed first. Each file is loaded with the `load` command, in the order

specified. `gnuplot` exits after the last file is processed. When no load

files are named, `gnuplot` enters into an interactive mode. The special

filename "-" is used to denote standard input. See "help batch/interactive"

for more details.

Many `gnuplot` commands have multiple options. These options must appear in

the proper order, although unwanted ones may be omitted in most cases. Thus

if the entire command is "command a b c", then "command a c" will probably

work, but "command c a" will fail.

Commands may extend over several input lines by ending each line but the last

with a backslash (\). The backslash must be the _last_ character on each

line. The effect is as if the backslash and newline were not there. That

is, no white space is implied, nor is a comment terminated. Therefore,

commenting out a continued line comments out the entire command (see

`comment`). But note that if an error occurs somewhere on a multi-line

command, the parser may not be able to locate precisely where the error is

and in that case will not necessarily point to the correct line.

In this document, curly braces (@{@}) denote optional arguments and a vertical

bar (|) separates mutually exclusive choices. `gnuplot` keywords or @ref{help}

topics are indicated by backquotes or `boldface` (where available). Angle

brackets (<>) are used to mark replaceable tokens. In many cases, a default

value of the token will be taken for optional arguments if the token is

omitted, but these cases are not always denoted with braces around the angle

brackets.

For on-line help on any topic, type @ref{help} followed by the name of the topic

or just @ref{help} or `?` to get a menu of available topics.

The new `gnuplot` user should begin by reading about `plotting` (if on-line,

type `help plotting`).

@uref{http://www.nas.nasa.gov/~woo/gnuplot/simple/simple.html,Simple Plots Demo }

@node Seeking-assistance, What's_New_in_version_3.7, Introduction, gnuplot

@section Seeking-assistance

@cindex seeking-assistance

There is a mailing list for `gnuplot` users. Note, however, that the

newsgroup

@example

comp.graphics.apps.gnuplot

@end example

is identical to the mailing list (they both carry the same set of messages).

We prefer that you read the messages through the newsgroup rather than

subscribing to the mailing list. Administrative requests should be sent to

@example

majordomo@@dartmouth.edu

@end example

Send a message with the body (not the subject) consisting of the single word

"help" (without the quotes) for more details.

The address for mailing to list members is:

@example

info-gnuplot@@dartmouth.edu

@end example

Bug reports and code contributions should be mailed to:

@example

bug-gnuplot@@dartmouth.edu

@end example

The list of those interested in beta-test versions is:

@example

info-gnuplot-beta@@dartmouth.edu

@end example

There is also a World Wide Web page with up-to-date information, including

known bugs:

@uref{http://www.cs.dartmouth.edu/gnuplot_info.html,http://www.cs.dartmouth.edu/gnuplot_info.html

}

Before seeking help, please check the

@uref{http://www.uni-karlsruhe.de/~ig25/gnuplot-faq.html,FAQ (Frequently Asked Questions) list.

}

If you do not have a copy of the FAQ, you may request a copy by email from

the Majordomo address above, ftp a copy from

@example

ftp://ftp.dartmouth.edu/pub/gnuplot

@end example

or see the WWW `gnuplot` page.

When posting a question, please include full details of the version of

`gnuplot`, the machine, and operating system you are using. A _small_ script

demonstrating the problem may be useful. Function plots are preferable to

datafile plots. If email-ing to info-gnuplot, please state whether or not

you are subscribed to the list, so that users who use news will know to email

a reply to you. There is a form for such postings on the WWW site.

@node What's_New_in_version_3.7, bind, Seeking-assistance, gnuplot

@section What's New in version 3.7

@cindex new-features

Gnuplot version 3.7 contains many new features. This section gives a partial

list and links to the new items in no particular order.

1. `fit f(x) 'file' via` uses the Marquardt-Levenberg method to fit data.

(This is only slightly different from the `gnufit` patch available for 3.5.)

2. Greatly expanded @ref{using} command. See @ref{using}.

3. @ref{timefmt} allows for the use of dates as input and output for time

series plots. See `Time/Date data` and

@uref{http://www.nas.nasa.gov/~woo/gnuplot/timefmt/timefmt.html,timedat.dem.

}

4. Multiline labels and font selection in some drivers.

5. Minor (unlabeled) tics. See @ref{mxtics}.

6. @ref{key} options for moving the key box in the page (and even outside of the

plot), putting a title on it and a box around it, and more. See @ref{key}.

7. Multiplots on a single logical page with @ref{multiplot}.

8. Enhanced `postscript` driver with super/subscripts and font changes.

(This was a separate driver (`enhpost`) that was available as a patch for

3.5.)

9. Second axes: use the top and right axes independently of the bottom and

left, both for plotting and labels. See @ref{plot}.

10. Special datafile names `'-'` and `""`. See @ref{special-filenames}.

11. Additional coordinate systems for labels and arrows. See `coordinates`.

12. @ref{size} can try to plot with a specified aspect ratio.

13. @ref{missing} now treats missing data correctly.

14. The @ref{call} command: `load` with arguments.

15. More flexible `range` commands with `reverse`, `writeback`, and `restore`

keywords.

16. @ref{encoding} for multi-lingual encoding.

17. New `x11` driver with persistent and multiple windows.

18. New plotting styles: @ref{xerrorbars}, @ref{errorlines}, @ref{yerrorlines},

@ref{xerrorlines}, @ref{xyerrorlines}, @ref{histeps}, @ref{financebars} and more.

See @ref{style}.

19. New tic label formats, including `"%l %L"` which uses the mantissa and

exponents to a given base for labels. See `set format`.

20. New drivers, including `cgm` for inclusion into MS-Office applications

and `gif` for serving plots to the WEB.

21. Smoothing and spline-fitting options for @ref{plot}. See @ref{smooth}.

22. @ref{margin} and @ref{origin} give much better control over where a

graph appears on the page.

23. @ref{border} now controls each border individually.

24. The new commands @ref{if} and @ref{reread} allow command loops.

25. Point styles and sizes, line types and widths can be specified on the

@ref{plot} command. Line types and widths can also be specified for grids,

borders, tics and arrows. See @ref{with}. Furthermore these types may be

combined and stored for further use. See `set style line`.

26. Text (labels, tic labels, and the time stamp) can be written vertically

by those terminals capable of doing so.

@node bind, Batch/Interactive_Operation, What's_New_in_version_3.7, gnuplot

@section bind

@c ?commands bind

@cindex bind

The @ref{bind} command allows to (re-)define a sequence of gnuplot commands

which will be executed when a certain key or key sequence is pressed

while the driver's window has the input focus.

Note that @ref{bind} is only available if gnuplot was compiled with mouse

support and it is used by all mouse-capable terminals.

Bindings overwrite the builtin bindings (like in every real editor),

except <space> and 'q' which cannot be rebound.

Mouse Buttons cannot be rebound.

Note that multikey-bindings with modifiers have to be quoted.

Syntax:

@example

bind [<key-sequence>] ["<gnuplot commands>"]

bind!

@end example

Examples:

- set bindings:

@example

bind a "replot"

bind "ctrl-a" "plot x*x"

bind "ctrl-alt-a" 'print "great"'

bind Home "set view 60,30; replot"

@end example

- show bindings:

@example

bind "ctrl-a" # shows the binding for ctrl-a

bind # shows all bindings

@end example

- remove bindings:

@example

bind "ctrl-alt-a" "" # removes binding for ctrl-alt-a

(note that builtins cannot be removed)

bind! # installs default (builtin) bindings

@end example

- bind a key to toggle something:

@example

v=0

bind "ctrl-r" "v=v+1;if(v%2)set term x11 noraise; else set term x11 raise"

@end example

Modifiers (ctrl / alt) are case insensitive, keys not:

@example

ctrl-alt-a == CtRl-alT-a

ctrl-alt-a != ctrl-alt-A

@end example

List of modifiers (alt == meta):

@example

ctrl, alt

@end example

List of supported special keys:

@example

"BackSpace", "Tab", "Linefeed", "Clear", "Return", "Pause", "Scroll_Lock",

"Sys_Req", "Escape", "Delete", "Home", "Left", "Up", "Right", "Down",

"PageUp", "PageDown", "End", "Begin",

@end example

@example

"KP_Space", "KP_Tab", "KP_Enter", "KP_F1", "KP_F2", "KP_F3", "KP_F4",

"KP_Home", "KP_Left", "KP_Up", "KP_Right", "KP_Down", "KP_PageUp",

"KP_PageDown", "KP_End", "KP_Begin", "KP_Insert", "KP_Delete", "KP_Equal",

"KP_Multiply", "KP_Add", "KP_Separator", "KP_Subtract", "KP_Decimal",

"KP_Divide",

@end example

@example

"KP_1" - "KP_9", "F1" - "F12"

@end example

see also @ref{mouse} and @ref{if}.

@node Batch/Interactive_Operation, Command-line-editing, bind, gnuplot

@section Batch/Interactive Operation

@cindex batch/interactive

`gnuplot` may be executed in either batch or interactive modes, and the two

may even be mixed together on many systems.

Any command-line arguments are assumed to be names of files containing

`gnuplot` commands (with the exception of standard X11 arguments, which are

processed first). Each file is loaded with the `load` command, in the order

specified. `gnuplot` exits after the last file is processed. When no load

files are named, `gnuplot` enters into an interactive mode. The special

filename "-" is used to denote standard input.

Both the @ref{exit} and @ref{quit} commands terminate the current command file and

`load` the next one, until all have been processed.

Examples:

To launch an interactive session:

@example

gnuplot

@end example

To launch a batch session using two command files "input1" and "input2":

@example

gnuplot input1 input2

@end example

To launch an interactive session after an initialization file "header" and

followed by another command file "trailer":

@example

gnuplot header - trailer

@end example

@node Command-line-editing, Comments, Batch/Interactive_Operation, gnuplot

@section Command-line-editing

@cindex line-editing

@cindex editing

@cindex history

@cindex command-line-editing

Command-line editing is supported by the Unix, Atari, VMS, MS-DOS and OS/2

versions of `gnuplot`. Also, a history mechanism allows previous commands to

be edited and re-executed. After the command line has been edited, a newline

or carriage return will enter the entire line without regard to where the

cursor is positioned.

(The readline function in `gnuplot` is not the same as the readline used in

GNU Bash and GNU Emacs. If the GNU version is desired, it may be selected

instead of the `gnuplot` version at compile time.)

The editing commands are as follows:

@example

`Line-editing`:

@end example

@example

^B moves back a single character.

^F moves forward a single character.

^A moves to the beginning of the line.

^E moves to the end of the line.

^H and DEL delete the previous character.

^D deletes the current character.

^K deletes from current position to the end of line.

^L,^R redraws line in case it gets trashed.

^U deletes the entire line.

^W deletes the last word.

@end example

@example

`History`:

@end example

@example

^P moves back through history.

^N moves forward through history.

@end example

On the IBM PC, the use of a TSR program such as DOSEDIT or CED may be desired

for line editing. The default makefile assumes that this is the case; by

default `gnuplot` will be compiled with no line-editing capability. If you

want to use `gnuplot`'s line editing, set READLINE in the makefile and add

readline.obj to the link file. The following arrow keys may be used on the

IBM PC and Atari versions if readline is used:

@example

Left Arrow - same as ^B.

Right Arrow - same as ^F.

Ctrl Left Arrow - same as ^A.

Ctrl Right Arrow - same as ^E.

Up Arrow - same as ^P.

Down Arrow - same as ^N.

@end example

The Atari version of readline defines some additional key aliases:

@example

Undo - same as ^L.

Home - same as ^A.

Ctrl Home - same as ^E.

Esc - same as ^U.

Help - @ref{help} plus return.

Ctrl Help - `help `.

@end example

@node Comments, Coordinates, Command-line-editing, gnuplot

@section Comments

@cindex comments

Comments are supported as follows: a `#` may appear in most places in a line

and `gnuplot` will ignore the rest of the line. It will not have this effect

inside quotes, inside numbers (including complex numbers), inside command

substitutions, etc. In short, it works anywhere it makes sense to work.

@node Coordinates, Environment, Comments, gnuplot

@section Coordinates

@cindex coordinates

The commands @ref{arrow}, @ref{key}, and @ref{label} allow you to draw

something at an arbitrary position on the graph. This position is specified

by the syntax:

@example

@{<system>@} <x>, @{<system>@} <y> @{,@{<system>@} <z>@}

@end example

Each <system> can either be `first`, `second`, `graph` or `screen`.

`first` places the x, y, or z coordinate in the system defined by the left

and bottom axes; `second` places it in the system defined by the second axes

(top and right); `graph` specifies the area within the axes---0,0 is bottom

left and 1,1 is top right (for splot, 0,0,0 is bottom left of plotting area;

use negative z to get to the base---see @ref{ticslevel}); and `screen`

specifies the screen area (the entire area---not just the portion selected by

@ref{size}), with 0,0 at bottom left and 1,1 at top right.

If the coordinate system for x is not specified, `first` is used. If the

system for y is not specified, the one used for x is adopted.

If one (or more) axis is timeseries, the appropriate coordinate should

be given as a quoted time string according to the @ref{timefmt} format string.

See @ref{xdata} and @ref{timefmt}. `gnuplot` will also accept an integer

expression, which will be interpreted as seconds from 1 January 2000.

@node Environment, Expressions, Coordinates, gnuplot

@section Environment

@cindex environment

A number of shell environment variables are understood by `gnuplot`. None of

these are required, but may be useful.

If GNUTERM is defined, it is used as the name of the terminal type to be

used. This overrides any terminal type sensed by `gnuplot` on start-up, but

is itself overridden by the .gnuplot (or equivalent) start-up file (see

`start-up`) and, of course, by later explicit changes.

On Unix, AmigaOS, AtariTOS, MS-DOS and OS/2, GNUHELP may be defined to be the

pathname of the HELP file (gnuplot.gih).

On VMS, the logical name GNUPLOT$HELP should be defined as the name of the

help library for `gnuplot`. The `gnuplot` help can be put inside any system

help library, allowing access to help from both within and outside `gnuplot`

if desired.

On Unix, HOME is used as the name of a directory to search for a .gnuplot

file if none is found in the current directory. On AmigaOS, AtariTOS,

MS-DOS and OS/2, gnuplot is used. On VMS, SYS$LOGIN: is used. See `help

start-up`.

On Unix, PAGER is used as an output filter for help messages.

On Unix, AtariTOS and AmigaOS, SHELL is used for the @ref{shell} command. On

MS-DOS and OS/2, COMSPEC is used for the @ref{shell} command.

On MS-DOS, if the BGI or Watcom interface is used, PCTRM is used to tell

the maximum resolution supported by your monitor by setting it to

S<max. horizontal resolution>. E.g. if your monitor's maximum resolution is

800x600, then use:

@example

set PCTRM=S800

@end example

If PCTRM is not set, standard VGA is used.

FIT_SCRIPT may be used to specify a `gnuplot` command to be executed when a

fit is interrupted---see `fit`. FIT_LOG specifies the filename of the

logfile maintained by fit.

GNUPLOT_LIB may be used to define additional search directories for data

and command files. The variable may contain a single directory name, or

a list of directories separated by a platform-specific path separator,

eg. ':' on Unix, or ';' on DOS/Windows/OS/2/Amiga platforms. The contents

of GNUPLOT_LIB are appended to the @ref{loadpath} variable, but not saved

with the @ref{save} and `save set` commands.

@node Expressions, Glossary, Environment, gnuplot

@section Expressions

@cindex expressions

In general, any mathematical expression accepted by C, FORTRAN, Pascal, or

BASIC is valid. The precedence of these operators is determined by the

specifications of the C programming language. White space (spaces and tabs)

is ignored inside expressions.

Complex constants are expressed as @{<real>,<imag>@}, where <real> and <imag>

must be numerical constants. For example, @{3,2@} represents 3 + 2i; @{0,1@}

represents 'i' itself. The curly braces are explicitly required here.

Note that gnuplot uses both "real" and "integer" arithmetic, like FORTRAN and

C. Integers are entered as "1", "-10", etc; reals as "1.0", "-10.0", "1e1",

3.5e-1, etc. The most important difference between the two forms is in

division: division of integers truncates: 5/2 = 2; division of reals does

not: 5.0/2.0 = 2.5. In mixed expressions, integers are "promoted" to reals

before evaluation: 5/2e0 = 2.5. The result of division of a negative integer

by a positive one may vary among compilers. Try a test like "print -5/2" to

determine if your system chooses -2 or -3 as the answer.

The integer expression "1/0" may be used to generate an "undefined" flag,

which causes a point to ignored; the `ternary` operator gives an example.

The real and imaginary parts of complex expressions are always real, whatever

the form in which they are entered: in @{3,2@} the "3" and "2" are reals, not

integers.

@menu

* Functions::

* Operators::

* User-defined::

@end menu

@node Functions, Operators, Expressions, Expressions

@subsection Functions

@c ?expressions functions

@cindex functions

@opindex functions

The functions in `gnuplot` are the same as the corresponding functions in

the Unix math library, except that all functions accept integer, real, and

complex arguments, unless otherwise noted.

For those functions that accept or return angles that may be given in either

degrees or radians (sin(x), cos(x), tan(x), asin(x), acos(x), atan(x),

atan2(x) and arg(z)), the unit may be selected by @ref{angles}, which

defaults to radians.

@menu

* abs::

* acos::

* acosh::

* arg::

* asin::

* asinh::

* atan::

* atan2::

* atanh::

* besj0::

* besj1::

* besy0::

* besy1::

* ceil::

* cos::

* cosh::

* erf::

* erfc::

* exp::

* floor::

* gamma::

* ibeta::

* inverf::

* igamma::

* imag::

* invnorm::

* int::

* lgamma::

* log::

* log10::

* norm::

* rand::

* real::

* sgn::

* sin::

* sinh::

* sqrt::

* tan::

* tanh::

* column::

* tm_hour::

* tm_mday::

* tm_min::

* tm_mon::

* tm_sec::

* tm_wday::

* tm_yday::

* tm_year::

* valid::

@end menu

@node abs, acos, Functions, Functions

@subsubsection abs

@c ?expressions functions abs

@c ?functions abs

@cindex abs

@findex abs

The `abs(x)` function returns the absolute value of its argument. The

returned value is of the same type as the argument.

For complex arguments, abs(x) is defined as the length of x in the complex

plane [i.e., sqrt(real(x)**2 + imag(x)**2) ].

@node acos, acosh, abs, Functions

@subsubsection acos

@c ?expressions functions acos

@c ?functions acos

@cindex acos

@findex acos

The `acos(x)` function returns the arc cosine (inverse cosine) of its

argument. `acos` returns its argument in radians or degrees, as selected by

@ref{angles}.

@node acosh, arg, acos, Functions

@subsubsection acosh

@c ?expressions functions acosh

@c ?functions acosh

@cindex acosh

@findex acosh

The `acosh(x)` function returns the inverse hyperbolic cosine of its argument

in radians.

@node arg, asin, acosh, Functions

@subsubsection arg

@c ?expressions functions arg

@c ?functions arg

@cindex arg

@findex arg

The `arg(x)` function returns the phase of a complex number in radians or

degrees, as selected by @ref{angles}.

@node asin, asinh, arg, Functions

@subsubsection asin

@c ?expressions functions asin

@c ?functions asin

@cindex asin

@findex asin

The `asin(x)` function returns the arc sin (inverse sin) of its argument.

`asin` returns its argument in radians or degrees, as selected by @ref{angles}.

@node asinh, atan, asin, Functions

@subsubsection asinh

@c ?expressions functions asinh

@c ?functions asinh

@cindex asinh

@findex asinh

The `asinh(x)` function returns the inverse hyperbolic sin of its argument in

radians.

@node atan, atan2, asinh, Functions

@subsubsection atan

@c ?expressions functions atan

@c ?functions atan

@cindex atan

@findex atan

The `atan(x)` function returns the arc tangent (inverse tangent) of its

argument. `atan` returns its argument in radians or degrees, as selected by

@ref{angles}.

@node atan2, atanh, atan, Functions

@subsubsection atan2

@c ?expressions functions atan2

@c ?functions atan2

@cindex atan2

@findex atan2

The `atan2(y,x)` function returns the arc tangent (inverse tangent) of the

ratio of the real parts of its arguments. @ref{atan2} returns its argument in

radians or degrees, as selected by @ref{angles}, in the correct quadrant.

@node atanh, besj0, atan2, Functions

@subsubsection atanh

@c ?expressions functions atanh

@c ?functions atanh

@cindex atanh

@findex atanh

The `atanh(x)` function returns the inverse hyperbolic tangent of its

argument in radians.

@node besj0, besj1, atanh, Functions

@subsubsection besj0

@c ?expressions functions besj0

@c ?functions besj0

@cindex besj0

@findex besj0

The `besj0(x)` function returns the j0th Bessel function of its argument.

@ref{besj0} expects its argument to be in radians.

@node besj1, besy0, besj0, Functions

@subsubsection besj1

@c ?expressions functions besj1

@c ?functions besj1

@cindex besj1

@findex besj1

The `besj1(x)` function returns the j1st Bessel function of its argument.

@ref{besj1} expects its argument to be in radians.

@node besy0, besy1, besj1, Functions

@subsubsection besy0

@c ?expressions functions besy0

@c ?functions besy0

@cindex besy0

@findex besy0

The @ref{besy0} function returns the y0th Bessel function of its argument.

@ref{besy0} expects its argument to be in radians.

@node besy1, ceil, besy0, Functions

@subsubsection besy1

@c ?expressions functions besy1

@c ?functions besy1

@cindex besy1

@findex besy1

The `besy1(x)` function returns the y1st Bessel function of its argument.

@ref{besy1} expects its argument to be in radians.

@node ceil, cos, besy1, Functions

@subsubsection ceil

@c ?expressions functions ceil

@c ?functions ceil

@cindex ceil

@findex ceil

The `ceil(x)` function returns the smallest integer that is not less than its

argument. For complex numbers, @ref{ceil} returns the smallest integer not less

than the real part of its argument.

@node cos, cosh, ceil, Functions

@subsubsection cos