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Formula:3958

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Digital Library of Mathematical Functions ID 10.20.E11

B k ⁢ ( ζ ) = - ζ - 1 2 ⁢ ∑ j = 0 2 ⁢ k + 1 ( 3 2 ) j ⁢ u j ⁢ ζ - 3 ⁢ j / 2 ⁢ U 2 ⁢ k - j + 1 ⁢ ( ( 1 - z 2 ) - 1 2 ) , subscript 𝐵 𝑘 𝜁 superscript 𝜁 1 2 superscript subscript 𝑗 0 2 𝑘 1 superscript 3 2 𝑗 subscript 𝑢 𝑗 superscript 𝜁 3 𝑗 2 subscript 𝑈 2 𝑘 𝑗 1 superscript 1 superscript 𝑧 2 1 2 {\displaystyle{\displaystyle B_{k}(\zeta)=-\zeta^{-\frac{1}{2}}\sum_{j=0}^{2k+% 1}(\tfrac{3}{2})^{j}u_{j}\zeta^{-3j/2}U_{2k-j+1}\left((1-z^{2})^{-\frac{1}{2}}% \right),}}


Constraint(s)

Symbols List

  • k 𝑘 {\displaystyle{\displaystyle k}} : nonnegative integer
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex variable
  • ζ ⁢ ( z ) 𝜁 𝑧 {\displaystyle{\displaystyle\zeta(z)}} : solution
  • u k subscript 𝑢 𝑘 {\displaystyle{\displaystyle u_{k}}} : constants
  • U k ⁢ ( p ) subscript 𝑈 𝑘 𝑝 {\displaystyle{\displaystyle U_{k}(p)}} : polynomial coefficient
  •  Edit this on Wikidata

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