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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.

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