Formula:5801

Digital Library of Mathematical Functions ID 15.9.E14

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

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
• ${\displaystyle{\displaystyle\cosh\NVar{z}}}$: hyperbolic cosine function
• ${\displaystyle{\displaystyle\operatorname{sech}\NVar{z}}}$: hyperbolic secant function
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle(\NVar{a},\NVar{b})}}$:
 

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