DLMF:10.49.E1 (Q3691)

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DLMF:10.49.E1
No description defined

    Statements

    Defining formula
    a k ⁢ ( n + 1 2 ) = { ( n + k ) ! 2 k ⁢ k ! ⁢ ( n - k ) ! , k = 0 , 1 , … , n , 0 , k = n + 1 , n + 2 , … . subscript 𝑎 𝑘 𝑛 1 2 cases 𝑛 𝑘 superscript 2 𝑘 𝑘 𝑛 𝑘 𝑘 0 1 … 𝑛 0 𝑘 𝑛 1 𝑛 2 … {\displaystyle{\displaystyle a_{k}(n+\tfrac{1}{2})=\begin{cases}\dfrac{(n+k)!}% {2^{k}k!(n-k)!},&k=0,1,\ldots,n,\\ 0,&k=n+1,n+2,\ldots.\end{cases}}}
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    DLMF id
    DLMF:10.49.E1
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    comment
    Warning: Falling back to standard tex;
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    Symbols used
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    Q11429
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1dec
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    Q11428
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1dec
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    expansion (locally)
    Defining formula
    a k ⁢ ( ν ) subscript 𝑎 𝑘 𝜈 {\displaystyle{\displaystyle a_{k}(\nu)}}
    xml-id
    C10.S17.XMD1.m1dec
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