DLMF:11.4.E1 (Q3933)

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DLMF:11.4.E1
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    Statements

    Defining formula
    𝐊 n + 1 2 ⁡ ( z ) = ( 2 π ⁢ z ) 1 2 ⁢ ∑ m = 0 n ( 2 ⁢ m ) ! ⁢  2 - 2 ⁢ m m ! ⁢ ( n - m ) ! ⁢ ( 1 2 ⁢ z ) n - 2 ⁢ m , associated-Struve-K 𝑛 1 2 𝑧 superscript 2 𝜋 𝑧 1 2 superscript subscript 𝑚 0 𝑛 2 𝑚 superscript  2 2 𝑚 𝑚 𝑛 𝑚 superscript 1 2 𝑧 𝑛 2 𝑚 {\displaystyle{\displaystyle\mathbf{K}_{n+\frac{1}{2}}\left(z\right)=\left(% \frac{2}{\pi z}\right)^{\frac{1}{2}}\sum_{m=0}^{n}\frac{(2m)!\,2^{-2m}}{m!\,(n% -m)!}\,(\tfrac{1}{2}z)^{n-2m},}}
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    DLMF id
    DLMF:11.4.E1
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    Symbols used
    Struve function
    Defining formula
    𝐊 ν ⁡ ( z ) associated-Struve-K 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{K}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E5.m2adec
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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.m2adec
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