special._precompute.gammainc_asy

Precompute coefficients of Temme’s asymptotic expansion for gammainc.

This takes about 8 hours to run on a 2.3 GHz Macbook Pro with 4GB ram.

Sources: [1] NIST, “Digital Library of Mathematical Functions”,

Module Contents

Functions

compute_a(n) a_k from DLMF 5.11.6
compute_g(n) g_k from DLMF 5.11.3/5.11.5
eta(lam) Function from DLMF 8.12.1 shifted to be centered at 0.
compute_alpha(n) alpha_n from DLMF 8.12.13
compute_d(K,N) d_{k, n} from DLMF 8.12.12
main()
compute_a(n)

a_k from DLMF 5.11.6

compute_g(n)

g_k from DLMF 5.11.3/5.11.5

eta(lam)

Function from DLMF 8.12.1 shifted to be centered at 0.

compute_alpha(n)

alpha_n from DLMF 8.12.13

compute_d(K, N)

d_{k, n} from DLMF 8.12.12

main()