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

Technical specifications
Filesystem library (filesystem TS)
Library fundamentals (library fundamentals TS)
Library fundamentals 2 (library fundamentals TS v2)
Library fundamentals 3 (library fundamentals TS v3)
Extensions for parallelism (parallelism TS)
Extensions for parallelism 2 (parallelism TS v2)
Extensions for concurrency (concurrency TS)
Concepts (concepts TS)
Ranges (ranges TS)
Mathematical special functions (special functions TR)
double      expint( double arg );

double      expint( float arg );
double      expint( long double arg );
float       expintf( float arg );

long double expintl( long double arg );
double      expint( IntegralType arg );
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.


[edit] Parameters

arg - value of a floating-point or Integral type

[edit] Return value

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

[edit] 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

[edit] 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

[edit] Example

(works as shown with gcc 6.0)

#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';


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

[edit] External links

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