Tanc function: Difference between revisions

Revision as of 20:38, 17 November 2022

Revision as of 20:39, 17 November 2022

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=== In terms of other special functions ===

* <math>\operatorname{Tanctanc}(z)={\frac {2\,i{{\rm KummerM}\left(1,\,2,\,2\,iz\right)}}{ \left( 2\,z+\pi

\right) {{\rm KummerM}\left(1,\,2,\,i \left( 2\,z+\pi \right) \right)}}}</math>, where <math>{\rm{KummerM}}(a,b,z)</math> is Kummer's [[confluent hypergeometric function]].

*<math>\operatorname{Tanctanc}(z)= \frac {2i \operatorname{HeunB} \left( 2,0,0,0,\sqrt {2}\sqrt {iz} \right) }{(2z+\pi) \operatorname{HeunB} \left( 2,0,0,0,\sqrt {2}\sqrt {(i/2) (2z+\pi) } \right) } </math>, where <math>{\rm{HeunB}}(q, \alpha, \gamma, \delta, \epsilon ,z)</math> is the biconfluent [[Heun function]].

* <math>\operatorname{Tanctanc}(z)= \frac {{\rm WhittakerM}(0,\,1/2,\,2\,iz)}{{\rm WhittakerM}(0,\,1/2,\,i (2z+\pi)) z} </math>, where <math>{\rm{WhittakerM}}(a,b,z)</math> is a [[Whittaker function]].

==Gallery==