DLMF:3.5.E37 (Q1292)

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DLMF:3.5.E37
No description defined

    Statements

    Defining formula
    ∫ c - i ⁢ ∞ c + i ⁢ ∞ e ζ ⁢ ζ - s ⁢ p k ⁢ ( 1 / ζ ) ⁢ p ℓ ⁢ ( 1 / ζ ) ⁢ d ζ = 0 , superscript subscript 𝑐 imaginary-unit 𝑐 imaginary-unit superscript 𝑒 𝜁 superscript 𝜁 𝑠 subscript 𝑝 𝑘 1 𝜁 subscript 𝑝 ℓ 1 𝜁 𝜁 0 {\displaystyle{\displaystyle\int_{c-\mathrm{i}\infty}^{c+\mathrm{i}\infty}e^{% \zeta}\zeta^{-s}p_{k}(1/\zeta)p_{\ell}(1/\zeta)\mathrm{d}\zeta=0,}}
    0 references
    DLMF id
    DLMF:3.5.E37
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    constraint
    k ≠ ℓ 𝑘 ℓ {\displaystyle{\displaystyle k\neq\ell}}
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    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aldec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aldec
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