repair_program.py

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535 bytes, as of the version from 2026-10-27 01:12 (current). Recorded here, not run.

import mpmath as mp

# Work at 150 decimal digits and print 100.
mp.mp.dps = 150
ell, eta = 0, 1
sigma = mp.im(mp.loggamma(ell + 1 + 1j*eta))
phase = mp.exp(mp.pi*eta/2 + 1j*(sigma - ell*mp.pi/2))

def G(rho):
    # Real part of the outgoing wave, DLMF 33.2.7 and 33.2.11.
    w = mp.whitw(-1j*eta, ell + mp.mpf('0.5'), -2j*rho)
    return mp.re(phase*w)

# For ell=0 and eta=1, the first positive zero lies in (3, 4).
# Numerical approximation; generate.py certifies the table.
root = mp.findroot(G, (3, 4))
print(mp.nstr(root, 100))