DLMF:10.6.E7 (Q3043)

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DLMF:10.6.E7
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    Statements

    Defining formula
    𝒞 ν ( k ) ⁡ ( z ) = 1 2 k ⁢ ∑ n = 0 k ( - 1 ) n ⁢ ( k n ) ⁢ 𝒞 ν - k + 2 ⁢ n ⁡ ( z ) . cylinder-function 𝜈 𝑘 𝑧 1 superscript 2 𝑘 superscript subscript 𝑛 0 𝑘 superscript 1 𝑛 binomial 𝑘 𝑛 cylinder-function 𝜈 𝑘 2 𝑛 𝑧 {\displaystyle{\displaystyle{\mathscr{C}_{\nu}^{(k)}}\left(z\right)=\frac{1}{2% ^{k}}\sum_{n=0}^{k}(-1)^{n}\genfrac{(}{)}{0.0pt}{}{k}{n}\mathscr{C}_{\nu-k+2n}% \left(z\right).}}
    0 references
    DLMF id
    DLMF:10.6.E7
    0 references
    Symbols used
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1adec
    0 references
    Q11430
    Defining formula
    𝒞 ν ⁡ ( z ) cylinder-function 𝜈 𝑧 {\displaystyle{\displaystyle\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.Px5.p1.m3acdec
    0 references
    Q11429
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1dec
    0 references
    Q11428
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1adec
    0 references
    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1fdec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1edec
    0 references
     
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