Module exponential_integrals 

Functions

Chi

This routine computes the integral Chi(x) := \Re[ \gamma_E + \log(x) + \int_0^x dt (\cosh(t)-1)/t] , where \gamma_E is the Euler constant (available as the macro M_EULER).

Chi_e

This routine computes the integral Chi(x) := \Re[ \gamma_E + \log(x) + \int_0^x dt (\cosh(t)-1)/t] , where \gamma_E is the Euler constant (available as the macro M_EULER).

Ci

This routine computes the Cosine integral Ci(x) = -\int_x^\infty dt \cos(t)/t for x > 0.

Ci_e

This routine computes the Cosine integral Ci(x) = -\int_x^\infty dt \cos(t)/t for x > 0.

E1

This routine computes the exponential integral E_1(x),

E2

This routine computes the second-order exponential integral E_2(x),

E1_e

This routine computes the exponential integral E_1(x),

E2_e

This routine computes the second-order exponential integral E_2(x),

Ei

This routine computes the exponential integral Ei(x),

Ei_e

This routine computes the exponential integral Ei(x),

En

This routine computes the exponential integral E_n(x) of order n,

En_e

This routine computes the exponential integral E_n(x) of order n,

Shi

This routine computes the integral Shi(x) = \int_0^x dt \sinh(t)/t.

Shi_e

This routine computes the integral Shi(x) = \int_0^x dt \sinh(t)/t.

Si

This routine computes the Sine integral Si(x) = \int_0^x dt \sin(t)/t.

Si_e

This routine computes the Sine integral Si(x) = \int_0^x dt \sin(t)/t.

_3

This routine computes the third-order exponential integral Ei_3(x) = \int_0^xdt \exp(-t^3) for x >= 0.

_3_e

This routine computes the third-order exponential integral Ei_3(x) = \int_0^xdt \exp(-t^3) for x >= 0.

atanint

This routine computes the Arctangent integral, which is defined as AtanInt(x) = \int_0^x dt \arctan(t)/t.

atanint_e

This routine computes the Arctangent integral, which is defined as AtanInt(x) = \int_0^x dt \arctan(t)/t.