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Formula:9665

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Digital Library of Mathematical Functions ID 30.16.E7

∑ j = 1 d e j , d 2 ⁢ ( n + m + 2 ⁢ j - 2 ⁢ p ) ! ( n - m + 2 ⁢ j - 2 ⁢ p ) ! ⁢ 1 2 ⁢ n + 4 ⁢ j - 4 ⁢ p + 1 = ( n + m ) ! ( n - m ) ! ⁢ 1 2 ⁢ n + 1 . superscript subscript 𝑗 1 𝑑 superscript subscript 𝑒 𝑗 𝑑 2 𝑛 𝑚 2 𝑗 2 𝑝 𝑛 𝑚 2 𝑗 2 𝑝 1 2 𝑛 4 𝑗 4 𝑝 1 𝑛 𝑚 𝑛 𝑚 1 2 𝑛 1 {\displaystyle{\displaystyle\sum_{j=1}^{d}e_{j,d}^{2}\frac{(n+m+2j-2p)!}{(n-m+% 2j-2p)!}\frac{1}{2n+4j-4p+1}=\frac{(n+m)!}{(n-m)!}\frac{1}{2n+1}.}}


Constraint(s)

Symbols List

  • ! {\displaystyle{\displaystyle!}} :
  • m 𝑚 {\displaystyle{\displaystyle m}} : nonnegative integer
  • n ≥ m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}} : integer degree
  • d 𝑑 {\displaystyle{\displaystyle d}} : dimension
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This page was last edited on 28 January 2024, at 11:02.
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