DLMF:31.10.E10 (Q9061)

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DLMF:31.10.E10
No description defined

    Statements

    Defining formula
    𝒦 ⁢ ( z , t ) = ( z ⁢ t - a ) 1 2 - δ - σ ⁢ F 1 2 ⁡ ( 1 2 - δ - σ + α , 1 2 - δ - σ + β γ ; z ⁢ t a ) ⁢ F 1 2 ⁡ ( - 1 2 + δ + σ , - 1 2 + ϵ - σ δ ; a ⁢ ( z - 1 ) ⁢ ( t - 1 ) ( a - 1 ) ⁢ ( z ⁢ t - a ) ) , 𝒦 𝑧 𝑡 superscript 𝑧 𝑡 𝑎 1 2 𝛿 𝜎 Gauss-hypergeometric-F-as-2F1 1 2 𝛿 𝜎 𝛼 1 2 𝛿 𝜎 𝛽 𝛾 𝑧 𝑡 𝑎 Gauss-hypergeometric-F-as-2F1 1 2 𝛿 𝜎 1 2 italic-ϵ 𝜎 𝛿 𝑎 𝑧 1 𝑡 1 𝑎 1 𝑧 𝑡 𝑎 {\displaystyle{\displaystyle\mathcal{K}(z,t)=(zt-a)^{\frac{1}{2}-\delta-\sigma% }\*{{}_{2}F_{1}}\left({\frac{1}{2}-\delta-\sigma+\alpha,\frac{1}{2}-\delta-% \sigma+\beta\atop\gamma};\frac{zt}{a}\right)\*{{}_{2}F_{1}}\left({-\frac{1}{2}% +\delta+\sigma,-\frac{1}{2}+\epsilon-\sigma\atop\delta};\frac{a(z-1)(t-1)}{(a-% 1)(zt-a)}\right),}}
    0 references
    DLMF id
    DLMF:31.10.E10
    0 references
    Symbols used
    Q11581
    Defining formula
    F 1 2 ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F-as-2F1 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}
    xml-id
    C16.S2.m5adec
    0 references
    Q12457
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C31.S1.XMD1.m1ddec
    0 references
    Q12458
    Defining formula
    γ 𝛾 {\displaystyle{\displaystyle\gamma}}
    xml-id
    C31.S1.XMD10.m1edec
    0 references
    Q12459
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C31.S1.XMD11.m1edec
    0 references
    Q12460
    Defining formula
    ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C31.S1.XMD12.m1edec
    0 references
    Q12461
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C31.S1.XMD6.m1ddec
    0 references
    Q12463
    Defining formula
    α 𝛼 {\displaystyle{\displaystyle\alpha}}
    xml-id
    C31.S1.XMD8.m1cdec
    0 references
    Q12464
    Defining formula
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    xml-id
    C31.S1.XMD9.m1cdec
    0 references
    kernel (locally)
    Defining formula
    𝒦 ⁢ ( z , t ) 𝒦 𝑧 𝑡 {\displaystyle{\displaystyle\mathcal{K}(z,t)}}
    xml-id
    C31.S10.XMD4.m1edec
    0 references
    Q12497
    Defining formula
    σ 𝜎 {\displaystyle{\displaystyle\sigma}}
    xml-id
    C31.S10.XMD8.m1adec
    0 references
     
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