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Diffstat (limited to 'gsl-1.9/doc/specfunc-expint.texi')
| -rw-r--r-- | gsl-1.9/doc/specfunc-expint.texi | 155 |
1 files changed, 155 insertions, 0 deletions
diff --git a/gsl-1.9/doc/specfunc-expint.texi b/gsl-1.9/doc/specfunc-expint.texi new file mode 100644 index 0000000..2d68ccb --- /dev/null +++ b/gsl-1.9/doc/specfunc-expint.texi @@ -0,0 +1,155 @@ +@cindex exponential integrals +@cindex integrals, exponential + +Information on the exponential integrals can be found in Abramowitz & +Stegun, Chapter 5. These functions are declared in the header file +@file{gsl_sf_expint.h}. + +@menu +* Exponential Integral:: +* Ei(x):: +* Hyperbolic Integrals:: +* Ei_3(x):: +* Trigonometric Integrals:: +* Arctangent Integral:: +@end menu + +@node Exponential Integral +@subsection Exponential Integral +@cindex E1(x), E2(x), Ei(x) + +@deftypefun double gsl_sf_expint_E1 (double @var{x}) +@deftypefunx int gsl_sf_expint_E1_e (double @var{x}, gsl_sf_result * @var{result}) +These routines compute the exponential integral @math{E_1(x)}, +@tex +\beforedisplay +$$ +E_1(x) := \Re \int_1^\infty dt \exp(-xt)/t. +$$ +\afterdisplay +@end tex +@ifinfo + +@example +E_1(x) := \Re \int_1^\infty dt \exp(-xt)/t. +@end example + +@end ifinfo +@noindent +@comment Domain: x != 0.0 +@comment Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW +@end deftypefun + +@deftypefun double gsl_sf_expint_E2 (double @var{x}) +@deftypefunx int gsl_sf_expint_E2_e (double @var{x}, gsl_sf_result * @var{result}) +These routines compute the second-order exponential integral @math{E_2(x)}, +@tex +\beforedisplay +$$ +E_2(x) := \Re \int_1^\infty dt \exp(-xt)/t^2. +$$ +\afterdisplay +@end tex +@ifinfo + +@example +E_2(x) := \Re \int_1^\infty dt \exp(-xt)/t^2. +@end example + +@end ifinfo +@noindent +@comment Domain: x != 0.0 +@comment Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW +@end deftypefun + +@node Ei(x) +@subsection Ei(x) + +@deftypefun double gsl_sf_expint_Ei (double @var{x}) +@deftypefunx int gsl_sf_expint_Ei_e (double @var{x}, gsl_sf_result * @var{result}) +These routines compute the exponential integral @math{Ei(x)}, +@tex +\beforedisplay +$$ +Ei(x) := - PV\left(\int_{-x}^\infty dt \exp(-t)/t\right) +$$ +\afterdisplay +@end tex +@ifinfo + +@example +Ei(x) := - PV(\int_@{-x@}^\infty dt \exp(-t)/t) +@end example + +@end ifinfo +@noindent +where @math{PV} denotes the principal value of the integral. +@comment Domain: x != 0.0 +@comment Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW +@end deftypefun + + +@node Hyperbolic Integrals +@subsection Hyperbolic Integrals +@cindex hyperbolic integrals +@cindex Shi(x) +@cindex Chi(x) + +@deftypefun double gsl_sf_Shi (double @var{x}) +@deftypefunx int gsl_sf_Shi_e (double @var{x}, gsl_sf_result * @var{result}) +These routines compute the integral @math{Shi(x) = \int_0^x dt \sinh(t)/t}. +@comment Exceptional Return Values: GSL_EOVRFLW, GSL_EUNDRFLW +@end deftypefun + + +@deftypefun double gsl_sf_Chi (double @var{x}) +@deftypefunx int gsl_sf_Chi_e (double @var{x}, gsl_sf_result * @var{result}) +These routines compute the integral @math{ Chi(x) := \Re[ \gamma_E + \log(x) + \int_0^x dt (\cosh[t]-1)/t] }, where @math{\gamma_E} is the Euler constant (available as the macro @code{M_EULER}). +@comment Domain: x != 0.0 +@comment Exceptional Return Values: GSL_EDOM, GSL_EOVRFLW, GSL_EUNDRFLW +@end deftypefun + + +@node Ei_3(x) +@subsection Ei_3(x) + +@deftypefun double gsl_sf_expint_3 (double @var{x}) +@deftypefunx int gsl_sf_expint_3_e (double @var{x}, gsl_sf_result * @var{result}) +These routines compute the third-order exponential integral +@math{Ei_3(x) = \int_0^xdt \exp(-t^3)} for @c{$x \ge 0$} +@math{x >= 0}. +@comment Exceptional Return Values: GSL_EDOM +@end deftypefun + +@node Trigonometric Integrals +@subsection Trigonometric Integrals +@cindex trigonometric integrals +@cindex Si(x) +@cindex Ci(x) +@deftypefun double gsl_sf_Si (const double @var{x}) +@deftypefunx int gsl_sf_Si_e (double @var{x}, gsl_sf_result * @var{result}) +These routines compute the Sine integral +@math{Si(x) = \int_0^x dt \sin(t)/t}. +@comment Exceptional Return Values: none +@end deftypefun + + +@deftypefun double gsl_sf_Ci (const double @var{x}) +@deftypefunx int gsl_sf_Ci_e (double @var{x}, gsl_sf_result * @var{result}) +These routines compute the Cosine integral @math{Ci(x) = -\int_x^\infty dt +\cos(t)/t} for @math{x > 0}. +@comment Domain: x > 0.0 +@comment Exceptional Return Values: GSL_EDOM +@end deftypefun + + +@node Arctangent Integral +@subsection Arctangent Integral +@cindex arctangent integral +@deftypefun double gsl_sf_atanint (double @var{x}) +@deftypefunx int gsl_sf_atanint_e (double @var{x}, gsl_sf_result * @var{result}) +These routines compute the Arctangent integral, which is defined as @math{AtanInt(x) = \int_0^x dt \arctan(t)/t}. +@comment Domain: +@comment Exceptional Return Values: +@end deftypefun + |