expint (MATLAB Function Reference)

Exponential integral

Syntax

Y = expint(X)

Definitions

The exponential integral is defined as:

Another common definition of the exponential integral function is the Cauchy principal value integral:

which, for real positive x, is related to expint as follows:

expint(-x+i*0) = -Ei(x) - i*pi
Ei(x) = real(-expint(-x))

Description

Y = expint(X)

evaluates the exponential integral for each element of X.

Algorithm

For elements of X in the domain

, expint uses a series expansion representation (equation 5.1.11 in [1]):

For all other elements of X, expint uses a continued fraction representation (equation 5.1.22 in [1]):

References

[1] Abramowitz, M. and I. A. Stegun. Handbook of Mathematical Functions. Chapter 5, New York: Dover Publications, 1965.

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