DLMF:30.3.E10 (Q8839)

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DLMF:30.3.E10
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    Statements

    Defining formula
    ℓ 6 = ( 4 ⁢ m 2 - 1 ) ⁢ ( ( n - m + 1 ) ⁢ ( n - m + 2 ) ⁢ ( n + m + 1 ) ⁢ ( n + m + 2 ) ( 2 ⁢ n - 1 ) ⁢ ( 2 ⁢ n + 1 ) ⁢ ( 2 ⁢ n + 3 ) 5 ⁢ ( 2 ⁢ n + 5 ) ⁢ ( 2 ⁢ n + 7 ) - ( n - m - 1 ) ⁢ ( n - m ) ⁢ ( n + m - 1 ) ⁢ ( n + m ) ( 2 ⁢ n - 5 ) ⁢ ( 2 ⁢ n - 3 ) ⁢ ( 2 ⁢ n - 1 ) 5 ⁢ ( 2 ⁢ n + 1 ) ⁢ ( 2 ⁢ n + 3 ) ) , subscript ℓ 6 4 superscript 𝑚 2 1 𝑛 𝑚 1 𝑛 𝑚 2 𝑛 𝑚 1 𝑛 𝑚 2 2 𝑛 1 2 𝑛 1 superscript 2 𝑛 3 5 2 𝑛 5 2 𝑛 7 𝑛 𝑚 1 𝑛 𝑚 𝑛 𝑚 1 𝑛 𝑚 2 𝑛 5 2 𝑛 3 superscript 2 𝑛 1 5 2 𝑛 1 2 𝑛 3 {\displaystyle{\displaystyle\ell_{6}=(4m^{2}-1)\left(\frac{(n-m+1)(n-m+2)(n+m+% 1)(n+m+2)}{(2n-1)(2n+1)(2n+3)^{5}(2n+5)(2n+7)}-\frac{(n-m-1)(n-m)(n+m-1)(n+m)}% {(2n-5)(2n-3)(2n-1)^{5}(2n+1)(2n+3)}\right),}}
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    DLMF id
    DLMF:30.3.E10
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    comment
    Warning: Falling back to standard tex;
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    Symbols used
    Q12408
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C30.S1.XMD4.m1hdec
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    Q12409
    Defining formula
    n ≥ m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}}
    xml-id
    C30.S1.XMD5.m1edec
    0 references
    Q12413
    Defining formula
    ℓ j subscript ℓ 𝑗 {\displaystyle{\displaystyle\ell_{j}}}
    xml-id
    C30.S3.XMD4.m1bdec
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