DLMF:11.10.E22 (Q4041)

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DLMF:11.10.E22
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    Statements

    Defining formula
    𝐄 n ⁡ ( z ) = - 𝐇 n ⁡ ( z ) + 1 π ⁢ ∑ k = 0 m 1 Γ ⁡ ( k + 1 2 ) Γ ⁡ ( n + 1 2 - k ) ⁢ ( 1 2 ⁢ z ) n - 2 ⁢ k - 1 , Weber-E 𝑛 𝑧 Struve-H 𝑛 𝑧 1 𝜋 superscript subscript 𝑘 0 subscript 𝑚 1 Euler-Gamma 𝑘 1 2 Euler-Gamma 𝑛 1 2 𝑘 superscript 1 2 𝑧 𝑛 2 𝑘 1 {\displaystyle{\displaystyle\mathbf{E}_{n}\left(z\right)=-\mathbf{H}_{n}\left(% z\right)+\frac{1}{\pi}\sum_{k=0}^{m_{1}}\frac{\Gamma\left(k+\tfrac{1}{2}\right% )}{\Gamma\left(n\!+\!\tfrac{1}{2}\!-\!k\right)}(\tfrac{1}{2}z)^{n-2k-1},}}
    0 references
    DLMF id
    DLMF:11.10.E22
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
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