Formula:5798

Digital Library of Mathematical Functions ID 15.9.E11

${\displaystyle{\displaystyle\phi^{(\alpha,\beta)}_{\lambda}\left(t\right)=F\left({\tfrac{1}{2}(\alpha+\beta+1-\mathrm{i}\lambda),\tfrac{1}{2}(\alpha+\beta+1+\mathrm{i}\lambda)\atop\alpha+1};-{\sinh^{2}}t\right).}}$

Symbols List

• ${\displaystyle{\displaystyle F\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)}}$: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
• ${\displaystyle{\displaystyle\sinh\NVar{z}}}$: hyperbolic sine function
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
 

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