NAME¶

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

Synopsis¶

double expint( double arg );

double expint( float arg );
double expint( long double arg ); (1)
float expintf( float arg );

long double expintl( long double arg );
double expint( IntegralType arg ); (2)

1) Computes the exponential integral of arg.
2) 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.