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Formula:3959

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Digital Library of Mathematical Functions ID 10.20.E12

C k ⁢ ( ζ ) = - ζ 1 2 ⁢ ∑ j = 0 2 ⁢ k + 1 ( 3 2 ) j ⁢ v j ⁢ ζ - 3 ⁢ j / 2 ⁢ V 2 ⁢ k - j + 1 ⁢ ( ( 1 - z 2 ) - 1 2 ) , subscript 𝐶 𝑘 𝜁 superscript 𝜁 1 2 superscript subscript 𝑗 0 2 𝑘 1 superscript 3 2 𝑗 subscript 𝑣 𝑗 superscript 𝜁 3 𝑗 2 subscript 𝑉 2 𝑘 𝑗 1 superscript 1 superscript 𝑧 2 1 2 {\displaystyle{\displaystyle C_{k}(\zeta)=-\zeta^{\frac{1}{2}}\sum_{j=0}^{2k+1% }(\tfrac{3}{2})^{j}v_{j}\zeta^{-3j/2}V_{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
  • v k subscript 𝑣 𝑘 {\displaystyle{\displaystyle v_{k}}} : constants
  • V k ⁢ ( p ) subscript 𝑉 𝑘 𝑝 {\displaystyle{\displaystyle V_{k}(p)}} : polynomial coefficient
  •  Edit this on Wikidata

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