Coshc function: Difference between revisions

Revision as of 05:06, 11 February 2023

Revision as of 04:46, 25 December 2023

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* <math>\operatorname{coshc}(z) = \frac {( iz+1/2\,\pi) {\rm M}(1,2,i\pi -2z)}{e^{(i/2)\pi -z} z} </math>, where <math>{\rm{M}}(a,b,z)</math> is Kummer's [[confluent hypergeometric function]].

*<math>\operatorname{coshc}(z)=\frac{1}{2}\,\frac {(2\,iz+\pi) \operatorname{HeunB} \left( 2,0,0,0,\sqrt {2}\sqrt {1/2\,i\pi -z} \right) } {e^{1/2\,i\pi -z}z} </math>, where <math>{\rm{HeunB}}(q, \alpha, \gamma, \delta, \epsilon ,z)</math> is the biconfluent [[Heun function]].

* <math>\operatorname{coshc}(z)= \frac {-i(2\,iz+\pi) {{\rm \mathbf WhittakerM}(0,\,1/2,\,i\pi -2z)}}{(4iz+2\pi) z}</math>, where <math>{\rm{WhittakerM}}(a,b,z)</math> is a [[Whittaker function]].

==Gallery==