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Formula:3960

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Digital Library of Mathematical Functions ID 10.20.E13

D k ⁢ ( ζ ) = ∑ j = 0 2 ⁢ k ( 3 2 ) j ⁢ u j ⁢ ζ - 3 ⁢ j / 2 ⁢ V 2 ⁢ k - j ⁢ ( ( 1 - z 2 ) - 1 2 ) . subscript 𝐷 𝑘 𝜁 superscript subscript 𝑗 0 2 𝑘 superscript 3 2 𝑗 subscript 𝑢 𝑗 superscript 𝜁 3 𝑗 2 subscript 𝑉 2 𝑘 𝑗 superscript 1 superscript 𝑧 2 1 2 {\displaystyle{\displaystyle D_{k}(\zeta)=\sum_{j=0}^{2k}(\tfrac{3}{2})^{j}u_{% j}\zeta^{-3j/2}V_{2k-j}\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
  • V k ⁢ ( p ) subscript 𝑉 𝑘 𝑝 {\displaystyle{\displaystyle V_{k}(p)}} : polynomial coefficient
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