Tanc function: Difference between revisions

Revision as of 12:02, 17 March 2015

Revision as of 12:06, 17 March 2015

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==In terms of other special functions==

* <math>\operatorname{Tanc}(z)=2\,{\frac {2\,i{{\rm KummerM}\left(1,\,2,\,2\,ziz\right)}}{ \left( 2\,izz+\pi
\right) {{\rm KummerM}\left(1,\,2,\,i\pi -2\,z)left( e^{2\,z-1/2\,i+\pi} \right) \right)}}}</math>

*<math>\operatorname{Tanc}(z)=2 {\frac {2\operatorname,i{HeunB}(2,0,0,0,\sqrt{2}it \sqrt{zHeunB})}{( 2iz+\pi) \operatorname{HeunB}left( 2,0,0,0,\sqrt {2} \sqrt {1/2iz} \,i\piright) -z}) e^{2\,z-1/2\,i\pi}} </math>

\left( 2\,z+\pi \right) {\it HeunB} \left( 2,0,0,0,\sqrt {2}\sqrt {1

/2\,i \left( 2\,z+\pi \right) } \right) }} </math>

* <math>\operatorname{Tanc}(z)= {\frac {{i{\rm \ WhittakerM}\left(0,\,1/2,\,2\,ziz\right)}}{
{{\rm WhittakerM}\left(0,\,1/2,\,i \pileft( -2\,z+\pi \right)} \right)}z}}
</math>

==Series expansion==