Negative integer order of the BesselI function #877
Description
mpmath version: 1.3.0
I am using mpmath to generate values for verification of my own complex Bessel function calculation routine.
https://github.com/tk-yoshimura/ComplexBessel
I have discovered that mpmath cannot compute for large negative integers in Bessel I functions, even though it can use the inversion formula.
https://dlmf.nist.gov/10.27
Example:
import mpmath as mpf
mpf.mp.dps = 64
x = 2
nus = [31, 32, 63, 64, 127, 128,
-31, -31.25, -32, -32.25,
-63, -63.25, -64, -64.25,
-127, -127.25, -128, -128.25
]
for nu in nus:
print(f"nu = {nu}, x = {x}")
try:
y = mpf.besseli(nu, x)
print(f"{mpf.nstr(y, 40, strip_zeros=False, min_fixed=2, max_fixed=1)}")
except ValueError as e:
print(e)
print("\n")Error Message:
nu = -127, x = 2
hypercomb() failed to converge to the requested 216 bits of accuracy
using a working precision of 4814 bits. The function value may be zero or
infinite; try passing zeroprec=N or infprec=M to bound finite values between
2^(-N) and 2^M. Otherwise try a higher maxprec or maxterms.