Coshc function: Difference between revisions

Revision as of 13:39, 18 March 2015

Revision as of 18:11, 18 March 2015

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==In terms of other special functions==

* <math>\operatorname{Coshc}(z)={\frac { \left( iz+1/2\,\pi \right)
{{\rm KummerMM}\left(1,\,2,\,i\pi -2\,z\right)}}{{{\rm e}^{1/2\,i\pi -z}}z}}
</math>

*<math>\operatorname{Coshc}(z)=\frac{1}{2}\,{\frac { \left( 2\,iz+\pi \right) {\it HeunB} \left( 2,0,0,0,\sqrt {2}\sqrt {z} \right) }{{

\sqrt {2}\sqrt {1/2\,i\pi -z} \right) }{{{\rm e}^{1/2\,i\pi -z}}z}}

{\rm e}^{z}}}} </math>

</math>

* <math>\operatorname{Coshc}(z)=1/2\, {\frac {{{\rm-i WhittakerM}\left(0,\,1/ 2,\,2iz+\,zpi \right)}}{z}} </math>

{{\rm \bf M}\left(0,\,1/2,\,i\pi -2\,z\right)}}{ \left( 4\,iz+2\,\pi

\right) z}}

</math>

==Series expansion==