DLMF:11.2.E1 (Q3916)

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DLMF:11.2.E1
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    Statements

    Defining formula
    𝐇 ν ⁡ ( z ) = ( 1 2 ⁢ z ) ν + 1 ⁢ ∑ n = 0 ∞ ( - 1 ) n ⁢ ( 1 2 ⁢ z ) 2 ⁢ n Γ ⁡ ( n + 3 2 ) ⁢ Γ ⁡ ( n + ν + 3 2 ) , Struve-H 𝜈 𝑧 superscript 1 2 𝑧 𝜈 1 superscript subscript 𝑛 0 superscript 1 𝑛 superscript 1 2 𝑧 2 𝑛 Euler-Gamma 𝑛 3 2 Euler-Gamma 𝑛 𝜈 3 2 {\displaystyle{\displaystyle\mathbf{H}_{\nu}\left(z\right)=(\tfrac{1}{2}z)^{% \nu+1}\sum_{n=0}^{\infty}\frac{(-1)^{n}(\tfrac{1}{2}z)^{2n}}{\Gamma\left(n+% \tfrac{3}{2}\right)\Gamma\left(n+\nu+\tfrac{3}{2}\right)},}}
    0 references
    DLMF id
    DLMF:11.2.E1
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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.m2adec
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    Q11491
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1dec
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    Q11492
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C11.S1.XMD3.m1dec
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    Q11493
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C11.S1.XMD4.m1dec
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