DLMF:11.4.E21 (Q3953)

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DLMF:11.4.E21
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    Statements

    test
    𝐇 0 ⁡ ( z ) = 4 π ⁢ ∑ k = 0 ∞ J 2 ⁢ k + 1 ⁡ ( z ) 2 ⁢ k + 1 = 2 ⁢ ∑ k = 0 ∞ ( - 1 ) k ⁢ J k + 1 2 2 ⁡ ( 1 2 ⁢ z ) , Struve-H 0 𝑧 4 𝜋 superscript subscript 𝑘 0 Bessel-J 2 𝑘 1 𝑧 2 𝑘 1 2 superscript subscript 𝑘 0 superscript 1 𝑘 Bessel-J 𝑘 1 2 2 1 2 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{0}\left(z\right)=\frac{4}{\pi}\sum_{k=% 0}^{\infty}\frac{J_{2k+1}\left(z\right)}{2k+1}=2\sum_{k=0}^{\infty}(-1)^{k}{J_% {k+\frac{1}{2}}^{2}}\left(\tfrac{1}{2}z\right),}}
    0 references
    DLMF id
    DLMF:11.4.E21
    0 references
    Symbols used
    Bessel function of the first kind
    test
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2addec
    0 references
    Struve function
    test
    𝐇 ν ⁡ ( z ) Struve-H 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E1.m2akdec
    0 references
     
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