DLMF:14.3.E1 (Q4690)

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DLMF:14.3.E1
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    Statements

    Defining formula
    𝖯 Ξ½ ΞΌ ⁑ ( x ) = ( 1 + x 1 - x ) ΞΌ / 2 ⁒ 𝐅 ⁑ ( Ξ½ + 1 , - Ξ½ ; 1 - ΞΌ ; 1 2 - 1 2 ⁒ x ) . Ferrers-Legendre-P-first-kind πœ‡ 𝜈 π‘₯ superscript 1 π‘₯ 1 π‘₯ πœ‡ 2 scaled-hypergeometric-bold-F 𝜈 1 𝜈 1 πœ‡ 1 2 1 2 π‘₯ {\displaystyle{\displaystyle\mathsf{P}^{\mu}_{\nu}\left(x\right)=\left(\frac{1% +x}{1-x}\right)^{\mu/2}\mathbf{F}\left(\nu+1,-\nu;1-\mu;\tfrac{1}{2}-\tfrac{1}% {2}x\right).}}
    0 references
    DLMF id
    DLMF:14.3.E1
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    Symbols used
    $$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function
    Defining formula
    𝐅 ⁑ ( a , b ; c ; z ) scaled-hypergeometric-bold-F π‘Ž 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z% }\right)}}
    xml-id
    C15.S2.E2.m2adec
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    Q11589
    Defining formula
    x π‘₯ {\displaystyle{\displaystyle x}}
    xml-id
    C14.S1.XMD1.m1dec
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    Q11591
    Defining formula
    ΞΌ πœ‡ {\displaystyle{\displaystyle\mu}}
    xml-id
    C14.S1.XMD7.m1dec
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    Q11590
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C14.S1.XMD8.m1dec
    0 references
     
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