Formula:5607

Digital Library of Mathematical Functions ID 14.18.E9

${\displaystyle{\displaystyle\mathsf{P}^{-\mu}_{\nu}\left(x\right)=\frac{\sin\left(\nu\pi\right)}{\pi}\sum_{n=0}^{\infty}(-1)^{n}\frac{2n+1}{(\nu-n)(\nu+n+1)}\mathsf{P}^{-\mu}_{n}\left(x\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\nu\notin\mathbb{Z}}}$
${\displaystyle{\displaystyle\mu\geq 0}}$
${\displaystyle{\displaystyle\nu\notin\mathbb{Z}}}$

Symbols List

• ${\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}\right)}}$: Ferrers function of the first kind
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\mathbb{Z}}}$:
• ${\displaystyle{\displaystyle\notin}}$:
• ${\displaystyle{\displaystyle\sin\NVar{z}}}$: sine function
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle\mu}}$: general order
• ${\displaystyle{\displaystyle\nu}}$: general degree
 

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