DLMF:11.7.E11 (Q4001)

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DLMF:11.7.E11
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    Statements

    Defining formula
    ∫ 0 ∞ t μ - ν - 1 ⁢ 𝐇 ν ⁡ ( t ) ⁢ d t = Γ ⁡ ( 1 2 ⁢ μ ) ⁢ 2 μ - ν - 1 ⁢ tan ⁡ ( 1 2 ⁢ π ⁢ μ ) Γ ⁡ ( ν - 1 2 ⁢ μ + 1 ) , superscript subscript 0 superscript 𝑡 𝜇 𝜈 1 Struve-H 𝜈 𝑡 𝑡 Euler-Gamma 1 2 𝜇 superscript 2 𝜇 𝜈 1 1 2 𝜋 𝜇 Euler-Gamma 𝜈 1 2 𝜇 1 {\displaystyle{\displaystyle\int_{0}^{\infty}t^{\mu-\nu-1}\mathbf{H}_{\nu}% \left(t\right)\mathrm{d}t=\frac{\Gamma\left(\tfrac{1}{2}\mu\right)2^{\mu-\nu-1% }\tan\left(\tfrac{1}{2}\pi\mu\right)}{\Gamma\left(\nu-\tfrac{1}{2}\mu+1\right)% },}}
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    DLMF id
    DLMF:11.7.E11
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    constraint
    | ℜ ⁡ μ | < 1 𝜇 1 {\displaystyle{\displaystyle|\Re\mu|<1}}
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    ℜ ⁡ ν > ℜ ⁡ μ - 3 2 𝜈 𝜇 3 2 {\displaystyle{\displaystyle\Re\nu>\Re\mu-\tfrac{3}{2}}}
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aedec
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    Struve function
    Defining formula
    𝐇 ν ⁡ ( z ) Struve-H 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E1.m2ahdec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2agdec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aidec
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