DLMF:15.2.E3 (Q4979)

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DLMF:15.2.E3
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    Statements

    Defining formula
    𝐅 ⁡ ( a , b c ; x + i ⁢ 0 ) - 𝐅 ⁡ ( a , b c ; x - i ⁢ 0 ) = 2 ⁢ π ⁢ i Γ ⁡ ( a ) ⁢ Γ ⁡ ( b ) ⁢ ( x - 1 ) c - a - b ⁢ 𝐅 ⁡ ( c - a , c - b c - a - b + 1 ; 1 - x ) , scaled-hypergeometric-bold-F 𝑎 𝑏 𝑐 𝑥 imaginary-unit 0 scaled-hypergeometric-bold-F 𝑎 𝑏 𝑐 𝑥 imaginary-unit 0 2 𝜋 imaginary-unit Euler-Gamma 𝑎 Euler-Gamma 𝑏 superscript 𝑥 1 𝑐 𝑎 𝑏 scaled-hypergeometric-bold-F 𝑐 𝑎 𝑐 𝑏 𝑐 𝑎 𝑏 1 1 𝑥 {\displaystyle{\displaystyle\mathbf{F}\left({a,b\atop c};x+\mathrm{i}0\right)-% \mathbf{F}\left({a,b\atop c};x-\mathrm{i}0\right)=\frac{2\pi\mathrm{i}}{\Gamma% \left(a\right)\Gamma\left(b\right)}(x-1)^{c-a-b}\mathbf{F}\left({c-a,c-b\atop c% -a-b+1};1-x\right),}}
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    DLMF id
    DLMF:15.2.E3
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    constraint
    x > 1 𝑥 1 {\displaystyle{\displaystyle x>1}}
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
    0 references
     
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