Formula:5799

Digital Library of Mathematical Functions ID 15.9.E12

${\displaystyle{\displaystyle\widetilde{f}(\lambda)=\int_{0}^{\infty}f(t)\phi^{(\alpha,\beta)}_{\lambda}\left(t\right)(2\sinh t)^{2\alpha+1}(2\cosh t)^{2\beta+1}\mathrm{d}t,}}$

Symbols List

• ${\displaystyle{\displaystyle\phi^{(\NVar{\alpha},\NVar{\beta})}_{\NVar{\lambda}}\left(\NVar{t}\right)}}$: Jacobi function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\cosh\NVar{z}}}$: hyperbolic cosine function
• ${\displaystyle{\displaystyle\sinh\NVar{z}}}$: hyperbolic sine function
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle f(t)}}$: function
 

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