2.3.E33 (Q723)

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2.3.E33
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    Statements

    DLMF defining formula
    F s ⁢ ( y ) = ∫ 0 ∞ exp ⁡ ( - 1 2 ⁢ τ 2 + y ⁢ τ ) ⁢ ( τ - y ) s ⁢ τ λ - 1 ⁢ d τ . subscript 𝐹 𝑠 𝑦 superscript subscript 0 1 2 superscript 𝜏 2 𝑦 𝜏 superscript 𝜏 𝑦 𝑠 superscript 𝜏 𝜆 1 𝜏 {\displaystyle{\displaystyle F_{s}(y)=\int_{0}^{\infty}\exp\left(-\tfrac{1}{2}% \tau^{2}+y\tau\right)(\tau-y)^{s}\tau^{\lambda-1}\mathrm{d}\tau.}}
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    Symbols used
    differential of x
    DLMF defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1apdec
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    exponential function
    DLMF defining formula
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2aedec
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    integral
    DLMF defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3apdec
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    positive constant
    DLMF defining formula
    λ 𝜆 {\displaystyle{\displaystyle\lambda}}
    xml-id
    C2.S3.XMD8.m1odec
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