DLMF:14.3.E21 (Q4710): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

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.m2amdec

Revision as of 00:20, 2 January 2020

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DLMF:14.3.E21
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    𝖯 ν μ ( x ) = 2 μ Γ ( 1 - 2 μ ) Γ ( ν + μ + 1 ) Γ ( ν - μ + 1 ) Γ ( 1 - μ ) ( 1 - x 2 ) μ / 2 C ν + μ ( 1 2 - μ ) ( x ) . Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 superscript 2 𝜇 Euler-Gamma 1 2 𝜇 Euler-Gamma 𝜈 𝜇 1 Euler-Gamma 𝜈 𝜇 1 Euler-Gamma 1 𝜇 superscript 1 superscript 𝑥 2 𝜇 2 ultraspherical-Gegenbauer-polynomial 1 2 𝜇 𝜈 𝜇 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\mu}_{\nu}\left(x\right)=\frac{2^{\mu}% \Gamma\left(1-2\mu\right)\Gamma\left(\nu+\mu+1\right)}{\Gamma\left(\nu-\mu+1% \right)\Gamma\left(1-\mu\right)\left(1-x^{2}\right)^{\mu/2}}C^{(\frac{1}{2}-% \mu)}_{\nu+\mu}\left(x\right).}}
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2amdec
    0 references