DLMF:15.9.E19 (Q5109)

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DLMF:15.9.E19
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    Statements

    Defining formula
    𝐅 ⁡ ( a , b a - b + 1 ; z ) = z ( b - a ) / 2 ⁢ ( 1 - z ) - b ⁢ P - b b - a ⁡ ( 1 + z 1 - z ) , scaled-hypergeometric-bold-F 𝑎 𝑏 𝑎 𝑏 1 𝑧 superscript 𝑧 𝑏 𝑎 2 superscript 1 𝑧 𝑏 Legendre-P-first-kind 𝑏 𝑎 𝑏 1 𝑧 1 𝑧 {\displaystyle{\displaystyle\mathbf{F}\left({a,b\atop a-b+1};z\right)=z^{% \ifrac{(b-a)}{2}}(1-z)^{-b}\*P^{b-a}_{-b}\left(\frac{1+z}{1-z}\right),}}
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    DLMF id
    DLMF:15.9.E19
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