DLMF:30.3#Ex9 (Q8838)

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DLMF:30.3#Ex9
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    2 4 = ( n - m - 1 ) ( n - m ) ( n + m - 1 ) ( n + m ) ( 2 n - 3 ) ( 2 n - 1 ) 3 ( 2 n + 1 ) - ( n - m + 1 ) ( n - m + 2 ) ( n + m + 1 ) ( n + m + 2 ) ( 2 n + 1 ) ( 2 n + 3 ) 3 ( 2 n + 5 ) . 2 subscript 4 𝑛 𝑚 1 𝑛 𝑚 𝑛 𝑚 1 𝑛 𝑚 2 𝑛 3 superscript 2 𝑛 1 3 2 𝑛 1 𝑛 𝑚 1 𝑛 𝑚 2 𝑛 𝑚 1 𝑛 𝑚 2 2 𝑛 1 superscript 2 𝑛 3 3 2 𝑛 5 {\displaystyle{\displaystyle 2\ell_{4}=\frac{(n-m-1)(n-m)(n+m-1)(n+m)}{(2n-3)(% 2n-1)^{3}(2n+1)}-\frac{(n-m+1)(n-m+2)(n+m+1)(n+m+2)}{(2n+1)(2n+3)^{3}(2n+5)}.}}
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