DLMF:15.9.E16 (Q5106)

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DLMF:15.9.E16
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    Statements

    Defining formula
    𝐅 ⁡ ( a , b 2 ⁢ b ; z ) = π Γ ⁡ ( b ) ⁢ z - b + ( 1 / 2 ) ⁢ ( 1 - z ) ( b - a - ( 1 / 2 ) ) / 2 ⁢ P a - b - ( 1 / 2 ) - b + ( 1 / 2 ) ⁡ ( 2 - z 2 ⁢ 1 - z ) , scaled-hypergeometric-bold-F 𝑎 𝑏 2 𝑏 𝑧 𝜋 Euler-Gamma 𝑏 superscript 𝑧 𝑏 1 2 superscript 1 𝑧 𝑏 𝑎 1 2 2 Legendre-P-first-kind 𝑏 1 2 𝑎 𝑏 1 2 2 𝑧 2 1 𝑧 {\displaystyle{\displaystyle\mathbf{F}\left({a,b\atop 2b};z\right)=\frac{\sqrt% {\pi}}{\Gamma\left(b\right)}z^{-b+(\ifrac{1}{2})}(1-z)^{(b-a-(\ifrac{1}{2}))/2% }\*P^{-b+(\ifrac{1}{2})}_{a-b-(\ifrac{1}{2})}\left(\frac{2-z}{2\sqrt{1-z}}% \right),}}
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    DLMF id
    DLMF:15.9.E16
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