DLMF:31.9.E2 (Q9044)

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DLMF:31.9.E2
No description defined

    Statements

    Defining formula
    ∫ ζ ( 1 + , 0 + , 1 - , 0 - ) t γ - 1 ⁢ ( 1 - t ) δ - 1 ⁢ ( t - a ) ϵ - 1 ⁢ w m ⁢ ( t ) ⁢ w k ⁢ ( t ) ⁢ d t = δ m , k ⁢ θ m . superscript subscript 𝜁 limit-from 1 limit-from 0 limit-from 1 limit-from 0 superscript 𝑡 𝛾 1 superscript 1 𝑡 𝛿 1 superscript 𝑡 𝑎 italic-ϵ 1 subscript 𝑤 𝑚 𝑡 subscript 𝑤 𝑘 𝑡 𝑡 Kronecker 𝑚 𝑘 subscript 𝜃 𝑚 {\displaystyle{\displaystyle\int_{\zeta}^{(1+,0+,1-,0-)}t^{\gamma-1}(1-t)^{% \delta-1}(t-a)^{\epsilon-1}\*w_{m}(t)w_{k}(t)\mathrm{d}t=\delta_{m,k}\theta_{m% }.}}
    0 references
    DLMF id
    DLMF:31.9.E2
    0 references
    Symbols used
    Q10768
    Defining formula
    δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}
    xml-id
    introduction.Sx4.p1.t1.r4.m5adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q12458
    Defining formula
    γ 𝛾 {\displaystyle{\displaystyle\gamma}}
    xml-id
    C31.S1.XMD10.m1adec
    0 references
    Q12459
    Defining formula
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C31.S1.XMD11.m1adec
    0 references
    Q12460
    Defining formula
    ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}}
    xml-id
    C31.S1.XMD12.m1dec
    0 references
    Q12483
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C31.S1.XMD4.m1adec
    0 references
    Q12461
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C31.S1.XMD6.m1adec
    0 references
    Q12491
    Defining formula
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C31.S9.XMD1.m1dec
    0 references
    normalization constant (locally)
    Defining formula
    θ m subscript 𝜃 𝑚 {\displaystyle{\displaystyle\theta_{m}}}
    xml-id
    C31.S9.XMD2.m1dec
    0 references
     
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