std::expint, std::expintf, std::expintl

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Technical Specifications

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Mathematical special functions

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double expint( double arg ); double expint( float arg ); double expint( long double arg ); float expintf( float arg ); long double expintl( long double arg );	(1)
double expint( IntegralType arg );	(2)

1) Computes the exponential integral of arg.

4) A set of overloads or a function template accepting an argument of any integral type. Equivalent to (1) after casting the argument to double.

As all special functions, expint is only guaranteed to be available in <cmath> if __STDCPP_MATH_SPEC_FUNCS__ is defined by the implementation to a value at least 201003L and if the user defines __STDCPP_WANT_MATH_SPEC_FUNCS__ before including any standard library headers.

Parameters

arg

-

value of a floating-point or Integral type

Return value

If no errors occur, value of the exponential integral of arg, that is -
-arg

e-t

t

dt, is returned.

Error handling

Errors may be reported as specified in math_errhandling

• If the argument is NaN, NaN is returned and domain error is not reported
• If the argument is 0, - is returned

Notes

Implementations that do not support TR 29124 but support TR 19768, provide this function in the header tr1/cmath and namespace std::tr1

An implementation of this function is also available in boost.math

Example

(works as shown with gcc 6.0)

Run this code

#define __STDCPP_WANT_MATH_SPEC_FUNCS__ 1
#include <cmath>
#include <iostream>
int main()
{
    std::cout << "Ei(0) = " << std::expint(0) << '\n'
              << "Ei(1) = " << std::expint(1) << '\n'
              << "Gompetz constant = " << -std::exp(1)*std::expint(-1) << '\n';
}

Output:

Ei(0) = -inf
Ei(1) = 1.89512
Gompetz constant = 0.596347

External links

Weisstein, Eric W. "Exponential Integral." From MathWorld--A Wolfram Web Resource.