SpecialFunctionsExponentialIntegral Method

public static double ExponentialIntegral(
	double x,
	int n
)

Parameters

x  Double

The argument of the Exponential Integral function.

n  Int32

Integer power of the denominator term. Generalization index.

Return Value

This implementation of the computation of the Exponential Integral function follows the derivation in "Handbook of Mathematical Functions, Applied Mathematics Series, Volume 55", Abramowitz, M., and Stegun, I.A. 1964, reprinted 1968 by Dover Publications, New York), Chapters 6, 7, and 26. AND "Advanced mathematical methods for scientists and engineers", Bender, Carl M.; Steven A. Orszag (1978). page 253

for x > 1 uses continued fraction approach that is often used to compute incomplete gamma. for 0 < x <= 1 uses Taylor series expansion

Our unit tests suggest that the accuracy of the Exponential Integral function is correct up to 13 floating point digits.

Reference