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Formula:9531

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Digital Library of Mathematical Functions ID 30.3.E10

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),}}


Constraint(s)

Symbols List

  • m 𝑚 {\displaystyle{\displaystyle m}} : nonnegative integer
  • n ≥ m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}} : integer degree
  • ℓ j subscript ℓ 𝑗 {\displaystyle{\displaystyle\ell_{j}}} : coefficients
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This page was last edited on 28 January 2024, at 11:02.
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