Formula:9667

Digital Library of Mathematical Functions ID 30.16.E9

${\displaystyle{\displaystyle\mathsf{Ps}^{m}_{n}\left(x,\gamma^{2}\right)=\lim_{d\to\infty}\sum_{j=1}^{d}(-1)^{j-p}e_{j,d}\mathsf{P}^{m}_{n+2(j-p)}\left(x\right).}}$

Symbols List

• ${\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: Ferrers function of the first kind
• ${\displaystyle{\displaystyle\mathsf{Ps}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},\NVar{\gamma^{2}}\right)}}$:
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle m}}$: nonnegative integer
• ${\displaystyle{\displaystyle n\geq m}}$: integer degree
• ${\displaystyle{\displaystyle d}}$: dimension
• ${\displaystyle{\displaystyle\gamma^{2}}}$: real parameter
 

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