DLMF:14.20.E4 (Q4925): 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.m2adec

Revision as of 13:32, 2 January 2020

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DLMF:14.20.E4
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    𝒲 { 𝖯 - 1 2 + i τ - μ ( x ) , 𝖯 - 1 2 + i τ - μ ( - x ) } = 2 | Γ ( μ + 1 2 + i τ ) | 2 ( 1 - x 2 ) . Wronskian Ferrers-Legendre-P-first-kind 𝜇 1 2 imaginary-unit 𝜏 𝑥 Ferrers-Legendre-P-first-kind 𝜇 1 2 imaginary-unit 𝜏 𝑥 2 superscript Euler-Gamma 𝜇 1 2 imaginary-unit 𝜏 2 1 superscript 𝑥 2 {\displaystyle{\displaystyle\mathscr{W}\left\{\mathsf{P}^{-\mu}_{-\frac{1}{2}+% \mathrm{i}\tau}\left(x\right),\mathsf{P}^{-\mu}_{-\frac{1}{2}+\mathrm{i}\tau}% \left(-x\right)\right\}=\frac{2}{|\Gamma\left(\mu+\frac{1}{2}+\mathrm{i}\tau% \right)|^{2}(1-x^{2})}.}}
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    DLMF:14.20.E4
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    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2adec
    0 references