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Difference between revisions of "cpp/numeric/special functions/expint"

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double      expint( double arg );
 
double      expint( double arg );
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[http://mathworld.wolfram.com/ExponentialIntegral.html Weisstein, Eric W. "Exponential Integral."] From MathWorld--A Wolfram Web Resource.
 
[http://mathworld.wolfram.com/ExponentialIntegral.html Weisstein, Eric W. "Exponential Integral."] From MathWorld--A Wolfram Web Resource.
  
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Revision as of 07:20, 29 November 2019

 
C++
 
Numerics library
Common mathematical functions
Mathematical special functions (C++17)
Mathematical constants (C++20)
Basic linear algebra algorithms (C++26)
Floating-point environment (C++11)
Complex numbers
Numeric array (valarray)
Pseudo-random number generation
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(C++17)
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Interpolations
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Saturation arithmetic
(C++26)
(C++26)
(C++26)
(C++26)
(C++26)

Generic numeric operations
Bit operations
(C++20)    
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++20)
(C++23)
(C++20)
 
Mathematical special functions
 
Defined in header <cmath>
double      expint( double arg );

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

long double expintl( long double arg );
 (1) (since C++17)
double      expint( IntegralType arg );
 (2) (since C++17)
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.

Contents

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 C++17, but support ISO 29124:2010, provide this function 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.

Implementations that do not support ISO 29124:2010 but support TR 19768:2007 (TR1), provide this function in the header tr1/cmath and namespace std::tr1.

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

Example

Run this code
#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.

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