DLMF:15.9.E17 (Q5107)

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DLMF:15.9.E17
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    Statements

    Defining formula
    𝐅 ⁡ ( a , a + 1 2 c ; z ) = 2 c - 1 ⁢ z ( 1 - c ) / 2 ⁢ ( 1 - z ) - a + ( ( c - 1 ) / 2 ) ⁢ P 2 ⁢ a - c 1 - c ⁡ ( 1 1 - z ) , scaled-hypergeometric-bold-F 𝑎 𝑎 1 2 𝑐 𝑧 superscript 2 𝑐 1 superscript 𝑧 1 𝑐 2 superscript 1 𝑧 𝑎 𝑐 1 2 Legendre-P-first-kind 1 𝑐 2 𝑎 𝑐 1 1 𝑧 {\displaystyle{\displaystyle\mathbf{F}\left({a,a+\tfrac{1}{2}\atop c};z\right)% =2^{c-1}z^{\ifrac{(1-c)}{2}}(1-z)^{-a+(\ifrac{(c-1)}{2})}\*P^{1-c}_{2a-c}\left% (\frac{1}{\sqrt{1-z}}\right),}}
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    DLMF id
    DLMF:15.9.E17
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