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DLMF:10.40.E9 - MaRDI portal

DLMF:10.40.E9 (Q4284)

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DLMF:10.40.E9
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    Statements

    DLMF defining formula
    α k ⁢ ( ν ) = ( 4 ⁢ ν 2 - 1 2 ) ⁢ ( 4 ⁢ ν 2 - 3 2 ) ⁢ ⋯ ⁢ ( 4 ⁢ ν 2 - ( 2 ⁢ k + 1 ) 2 ) ( k + 1 ) ! ⁢ ( 1 4 ⁢ ν 2 - 1 2 + 1 4 ⁢ ν 2 - 3 2 + ⋯ + 1 4 ⁢ ν 2 - ( 2 ⁢ k + 1 ) 2 ) . subscript 𝛼 𝑘 𝜈 4 superscript 𝜈 2 superscript 1 2 4 superscript 𝜈 2 superscript 3 2 ⋯ 4 superscript 𝜈 2 superscript 2 𝑘 1 2 𝑘 1 1 4 superscript 𝜈 2 superscript 1 2 1 4 superscript 𝜈 2 superscript 3 2 ⋯ 1 4 superscript 𝜈 2 superscript 2 𝑘 1 2 {\displaystyle{\displaystyle\alpha_{k}(\nu)=\frac{(4\nu^{2}-1^{2})(4\nu^{2}-3^% {2})\cdots(4\nu^{2}-(2k+1)^{2})}{(k+1)!}\*\left(\frac{1}{4\nu^{2}-1^{2}}+\frac% {1}{4\nu^{2}-3^{2}}+\cdots+\frac{1}{4\nu^{2}-(2k+1)^{2}}\right).}}
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    comment
    Warning: Falling back to standard tex;
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    Symbols used
    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    nonnegative integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1fdec
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    complex parameter
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1hdec
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    Identifiers

     
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