Formula:5425

Digital Library of Mathematical Functions ID 14.5.E16

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "TeX input is invalid."): {\displaystyle \assLegendreP[-1/2]{\nu}@{\cosh@@{\xi}}=\left(\frac{2}{\pi\sinh@@{\xi}}\right)^{1/2}\frac{\sinh@{\left(\nu+\frac{1}{2}\right)\xi}}{\nu+\frac{1}{2}},}

Symbols List

• ${\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}$: associated Legendre function of the first kind
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\cosh\NVar{z}}}$: hyperbolic cosine function
• ${\displaystyle{\displaystyle\sinh\NVar{z}}}$: hyperbolic sine function
• ${\displaystyle{\displaystyle\nu}}$: general degree
• ${\displaystyle{\displaystyle\xi>0}}$: variable
 

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