DLMF:14.8.E2 (Q4776): Difference between revisions

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ν m - 1 , m - 2 , , - m 𝜈 𝑚 1 𝑚 2 𝑚 {\displaystyle{\displaystyle\nu\neq m-1,m-2,\dots,-m}}

\nu\neq m-1,m-2,\dots,-m
Property / constraint: ν m - 1 , m - 2 , , - m 𝜈 𝑚 1 𝑚 2 𝑚 {\displaystyle{\displaystyle\nu\neq m-1,m-2,\dots,-m}} / rank
 
Normal rank

Revision as of 17:51, 30 December 2019

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DLMF:14.8.E2
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    𝖯 ν m ( x ) ( - 1 ) m ( ν - m + 1 ) 2 m m ! ( 1 - x 2 ) m / 2 , asymptotically-equals Ferrers-Legendre-P-first-kind 𝑚 𝜈 𝑥 superscript 1 𝑚 Pochhammer 𝜈 𝑚 1 2 𝑚 𝑚 superscript 1 𝑥 2 𝑚 2 {\displaystyle{\displaystyle\mathsf{P}^{m}_{\nu}\left(x\right)\sim(-1)^{m}% \frac{{\left(\nu-m+1\right)_{2m}}}{m!}\left(\frac{1-x}{2}\right)^{m/2},}}
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    DLMF:14.8.E2
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    ν m - 1 , m - 2 , , - m 𝜈 𝑚 1 𝑚 2 𝑚 {\displaystyle{\displaystyle\nu\neq m-1,m-2,\dots,-m}}
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