DLMF:11.5.E9 (Q3976)

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DLMF:11.5.E9
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    Statements

    Defining formula
    ( 1 2 ⁢ z ) - ν - 1 ⁢ 𝐋 ν ⁡ ( z ) = 1 2 ⁢ π ⁢ i ⁢ ∫ ∞ ( 0 + ) π ⁢ csc ⁡ ( π ⁢ s ) Γ ⁡ ( 3 2 + s ) ⁢ Γ ⁡ ( 3 2 + ν + s ) ⁢ ( - 1 4 ⁢ z 2 ) s ⁢ d s . superscript 1 2 𝑧 𝜈 1 modified-Struve-L 𝜈 𝑧 1 2 𝜋 𝑖 superscript subscript limit-from 0 𝜋 𝜋 𝑠 Euler-Gamma 3 2 𝑠 Euler-Gamma 3 2 𝜈 𝑠 superscript 1 4 superscript 𝑧 2 𝑠 𝑠 {\displaystyle{\displaystyle(\tfrac{1}{2}z)^{-\nu-1}\mathbf{L}_{\nu}\left(z% \right)=\frac{1}{2\pi i}\int_{\infty}^{(0+)}\frac{\pi\csc\left(\pi s\right)}{% \Gamma\left(\tfrac{3}{2}+s\right)\Gamma\left(\tfrac{3}{2}+\nu+s\right)}(-% \tfrac{1}{4}z^{2})^{s}\mathrm{d}s.}}
    0 references
    DLMF id
    DLMF:11.5.E9
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2afdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
    0 references
    cosecant function
    Defining formula
    csc ⁡ z 𝑧 {\displaystyle{\displaystyle\csc\NVar{z}}}
    xml-id
    C4.S14.E5.m2aadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
    0 references
    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.m3ahdec
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    modified Struve function
    Defining formula
    𝐋 ν ⁡ ( z ) modified-Struve-L 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{L}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E2.m2abdec
    0 references
     
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