DLMF:14.20.E4 (Q4925): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11591 / rank
 
Normal rank
Property / Symbols used: Q11591 / qualifier
 
Defining formula:

μ 𝜇 {\displaystyle{\displaystyle\mu}}

\mu
Property / Symbols used: Q11591 / qualifier
 
xml-id: C14.S1.XMD7.m1cdec

Latest revision as of 13:32, 2 January 2020

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DLMF:14.20.E4
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    Statements

    Defining formula
    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})}.}}
    0 references
    DLMF id
    DLMF:14.20.E4
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Ferrers function of the first kind
    Defining formula
    𝖯 ν μ ⁡ ( x ) Ferrers-Legendre-P-first-kind 𝜇 𝜈 𝑥 {\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C14.S3.E1.m2abdec
    0 references
    Q10865
    Defining formula
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    Q11589
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1cdec
    0 references
    Q11630
    Defining formula
    τ 𝜏 {\displaystyle{\displaystyle\tau}}
    xml-id
    C14.S1.XMD3.m1cdec
    0 references
    Q11591
    Defining formula
    μ 𝜇 {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1cdec
    0 references
     
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