Exponential Integrals
=====================

Exponential Integrals
---------------------

We have E_1(x) := Re \int_1^\infty dt \exp(-xt)/t ; E_2(x) := Re \int_1^\infty dt \exp(-xt)/t^2 .

 -- Function: int gsl_sf_expint_E1_impl (double x, gsl_sf_result * result)
 -- Function: int gsl_sf_expint_E1_e (double x, gsl_sf_result * result)
     Domain: x != 0.0 Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW

 -- Function: int gsl_sf_expint_E2_impl (double x, gsl_sf_result * result)
 -- Function: int gsl_sf_expint_E2_e (double x, gsl_sf_result * result)
     Domain: x != 0.0 Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW

Ei(x)
-----

We have Ei(x) := PV \int_(-x)^\infty dt \exp(-t)/t .

 -- Function: int gsl_sf_expint_Ei_impl (double x, gsl_sf_result * result)
 -- Function: int gsl_sf_expint_Ei_e (double x, gsl_sf_result * result)
     Domain: x != 0.0 Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW

Hyperbolic Integrals
--------------------

We have Shi(x) = \int_0^x dt \sinh(t)/t ; Chi(x) := Re[ M_EULER + log(x) + \int_0^x dt (Cosh[t]-1)/t .

 -- Function: int gsl_sf_Shi_impl (double x, gsl_sf_result * result)
 -- Function: int gsl_sf_Shi_e (double x, gsl_sf_result * result)
     Exceptional Return Values: GSL_EOVRFLW, GSL_EUNDRFLW

 -- Function: int gsl_sf_Chi_impl (double x, gsl_sf_result * result)
 -- Function: int gsl_sf_Chi_e (double x, gsl_sf_result * result)
     Domain: x != 0.0 Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW

Ei_3(x)
-------

We have Ei_3(x) = \int_0^x dt \exp(-t^3) .

 -- Function: int gsl_sf_expint_3_impl (double x, gsl_sf_result * result)
 -- Function: int gsl_sf_expint_3_e (double x, gsl_sf_result * result)
     Domain: x >= 0.0 Exceptional Return Values: GSL_EDOM

Trigonometric Integrals
-----------------------

We have Si(x) = \int_0^x dt \sin(t)/t ; Ci(x) = -\int_x^\infty \cos(t)/t .

 -- Function: int gsl_sf_Si_impl (const double x, gsl_sf_result * result)
 -- Function: int gsl_sf_Si_e (double x, gsl_sf_result * result)
     Exceptional Return Values: none

 -- Function: int gsl_sf_Ci_impl (const double x, gsl_sf_result * result)
 -- Function: int gsl_sf_Ci_e (double x, gsl_sf_result * result)
     Domain: x > 0.0 Exceptional Return Values: GSL_EDOM

Arctangent Integral
-------------------

We have AtanInt(x) = \int_0^x dt \arctan(t)/t .

 -- Function: int gsl_sf_atanint_impl (double x, gsl_sf_result * result);
 -- Function: int gsl_sf_atanint_e (double x, gsl_sf_result * result);
     Domain: Exceptional Return Values: