DLMF:15.9.E21 (Q5111)

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DLMF:15.9.E21
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    Statements

    Defining formula
    𝐅 ⁡ ( a , 1 - a c ; z ) = ( - z 1 - z ) ( 1 - c ) / 2 ⁢ P - a 1 - c ⁡ ( 1 - 2 ⁢ z ) , scaled-hypergeometric-bold-F 𝑎 1 𝑎 𝑐 𝑧 superscript 𝑧 1 𝑧 1 𝑐 2 Legendre-P-first-kind 1 𝑐 𝑎 1 2 𝑧 {\displaystyle{\displaystyle\mathbf{F}\left({a,1-a\atop c};z\right)=\left(% \frac{-z}{1-z}\right)^{\ifrac{(1-c)}{2}}\*P^{1-c}_{-a}\left(1-2z\right),}}
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    DLMF id
    DLMF:15.9.E21
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    constraint
    | ph ⁡ ( - z ) | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle\left|\operatorname{ph}\left(-z\right)\right|<\pi}}
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