DLMF:11.4.E19 (Q3951)

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DLMF:11.4.E19
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    Statements

    Defining formula
    𝐇 ν ⁡ ( z ) = ( z 2 ⁢ π ) 1 / 2 ⁢ ∑ k = 0 ∞ ( 1 2 ⁢ z ) k k ! ⁢ ( k + 1 2 ) ⁢ J k + ν + 1 2 ⁡ ( z ) , Struve-H 𝜈 𝑧 superscript 𝑧 2 𝜋 1 2 superscript subscript 𝑘 0 superscript 1 2 𝑧 𝑘 𝑘 𝑘 1 2 Bessel-J 𝑘 𝜈 1 2 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{\nu}\left(z\right)=\left(\frac{z}{2\pi% }\right)^{1/2}\sum_{k=0}^{\infty}\frac{(\tfrac{1}{2}z)^{k}}{k!(k+\tfrac{1}{2})% }J_{k+\nu+\frac{1}{2}}\left(z\right),}}
    0 references
    DLMF id
    DLMF:11.4.E19
    0 references
    Symbols used
    Bessel function of the first kind
    Defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2abdec
    0 references
     
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