DLMF:11.10.E23 (Q4739)

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DLMF:11.10.E23
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    Statements

    DLMF defining formula
    𝐄 - n ⁡ ( z ) = - 𝐇 - n ⁡ ( z ) + ( - 1 ) n + 1 π ⁢ ∑ k = 0 m 2 Γ ⁡ ( n - k - 1 2 ) Γ ⁡ ( k + 3 2 ) ⁢ ( 1 2 ⁢ z ) - n + 2 ⁢ k + 1 , Weber-E 𝑛 𝑧 Struve-H 𝑛 𝑧 superscript 1 𝑛 1 𝜋 superscript subscript 𝑘 0 subscript 𝑚 2 Euler-Gamma 𝑛 𝑘 1 2 Euler-Gamma 𝑘 3 2 superscript 1 2 𝑧 𝑛 2 𝑘 1 {\displaystyle{\displaystyle\mathbf{E}_{-n}\left(z\right)=-\mathbf{H}_{-n}% \left(z\right)+\frac{(-1)^{n+1}}{\pi}\sum_{k=0}^{m_{2}}\frac{\Gamma\left(n\!-% \!k\!-\!\tfrac{1}{2}\right)}{\Gamma\left(k+\tfrac{3}{2}\right)}(\tfrac{1}{2}z)% ^{-n+2k+1},}}
    0 references
    Symbols used
    gamma function
    DLMF defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2acdec
    0 references
    Struve function
    DLMF defining formula
    𝐇 ν ⁡ ( z ) Struve-H 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{H}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S2.E1.m2aadec
    0 references
    Weber function
    DLMF defining formula
    𝐄 ν ⁡ ( z ) Weber-E 𝜈 𝑧 {\displaystyle{\displaystyle\mathbf{E}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C11.S10.E2.m2andec
    0 references
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ardec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C11.S1.XMD2.m1vdec
    0 references
    integer order
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C11.S1.XMD4.m1adec
    0 references
    nonnegative integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C11.S1.XMD5.m1cdec
    0 references

    Identifiers

     
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