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The efficient computation of some generalised exponential integrals. (English) Zbl 1013.65017

Summary: The accurate and efficient computation of the special functions G k (x) is discussed, where

G k (x)=1 (k-1)! 1 exp(-xy)(logy) k-1 dy y·

These functions appear in the computation of the derivatives of the L-series of an elliptic curve, and in radiative transfer problems from astrophysics. By dividing (0,) into 3 sub-intervals, we derive Chebyshev polynomial expansions for Gk, k=1,,4 with the coefficients given to an accuracy of 20 decimal places.

MSC:
65D20Computation of special functions, construction of tables
33C60Hypergeometric integrals and functions defined by them
33F05Numerical approximation and evaluation of special functions