DLMF:14.5.E2 (Q4714): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
Defining formula:

Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2aadec

Revision as of 01:21, 2 January 2020

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DLMF:14.5.E2
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    d 𝖯 ν μ ( x ) d x | x = 0 = - 2 μ + 1 π 1 / 2 Γ ( 1 2 ν - 1 2 μ + 1 2 ) Γ ( - 1 2 ν - 1 2 μ ) , evaluated-at derivative Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 𝑥 𝑥 0 superscript 2 𝜇 1 superscript 𝜋 1 2 Euler-Gamma 1 2 𝜈 1 2 𝜇 1 2 Euler-Gamma 1 2 𝜈 1 2 𝜇 {\displaystyle{\displaystyle\left.\frac{\mathrm{d}\mathsf{P}^{\mu}_{\nu}\left(% x\right)}{\mathrm{d}x}\right|_{x=0}=-\frac{2^{\mu+1}\pi^{1/2}}{\Gamma\left(% \frac{1}{2}\nu-\frac{1}{2}\mu+\frac{1}{2}\right)\Gamma\left(-\frac{1}{2}\nu-% \frac{1}{2}\mu\right)},}}
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    DLMF:14.5.E2
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2aadec
    0 references