DLMF:15.9.E18 (Q5108)

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DLMF:15.9.E18
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    Statements

    test
    𝐅 ⁡ ( a , b a + b + 1 2 ; z ) = 2 a + b - ( 1 / 2 ) ⁢ ( - z ) ( - a - b + ( 1 / 2 ) ) / 2 ⁢ P a - b - ( 1 / 2 ) - a - b + ( 1 / 2 ) ⁡ ( 1 - z ) , scaled-hypergeometric-bold-F 𝑎 𝑏 𝑎 𝑏 1 2 𝑧 superscript 2 𝑎 𝑏 1 2 superscript 𝑧 𝑎 𝑏 1 2 2 Legendre-P-first-kind 𝑎 𝑏 1 2 𝑎 𝑏 1 2 1 𝑧 {\displaystyle{\displaystyle\mathbf{F}\left({a,b\atop a+b+\tfrac{1}{2}};z% \right)=2^{a+b-(\ifrac{1}{2})}(-z)^{(-a-b+(\ifrac{1}{2}))/2}\*P^{-a-b+(\ifrac{% 1}{2})}_{a-b-(\ifrac{1}{2})}\left(\sqrt{1-z}\right),}}
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    DLMF id
    DLMF:15.9.E18
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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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