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Formula:9289

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Digital Library of Mathematical Functions ID 29.3.E10

β p - H - α p - 1 ⁢ γ p β p - 1 - H - α p - 2 ⁢ γ p - 1 β p - 2 - H - ⁢ … = α p ⁢ γ p + 1 β p + 1 - H - α p + 1 ⁢ γ p + 2 β p + 2 - H - ⁢ ⋯ , subscript 𝛽 𝑝 𝐻 continued-fraction subscript 𝛼 𝑝 1 subscript 𝛾 𝑝 subscript 𝛽 𝑝 1 𝐻 continued-fraction subscript 𝛼 𝑝 2 subscript 𝛾 𝑝 1 subscript 𝛽 𝑝 2 limit-from 𝐻 … continued-fraction subscript 𝛼 𝑝 subscript 𝛾 𝑝 1 subscript 𝛽 𝑝 1 𝐻 continued-fraction subscript 𝛼 𝑝 1 subscript 𝛾 𝑝 2 subscript 𝛽 𝑝 2 limit-from 𝐻 ⋯ {\displaystyle{\displaystyle\beta_{p}-H-\cfrac{\alpha_{p-1}\gamma_{p}}{\beta_{% p-1}-H-\cfrac{\alpha_{p-2}\gamma_{p-1}}{\beta_{p-2}-H-}}\dots=\cfrac{\alpha_{p% }\gamma_{p+1}}{\beta_{p+1}-H-\cfrac{\alpha_{p+1}\gamma_{p+2}}{\beta_{p+2}-H-}}% \cdots,}}


Constraint(s)

Symbols List

  • p 𝑝 {\displaystyle{\displaystyle p}} : nonnegative integer
  • H 𝐻 {\displaystyle{\displaystyle H}} : 29.3.E9
  • α p subscript 𝛼 𝑝 {\displaystyle{\displaystyle\alpha_{p}}} : 29.3.E11
  • β p subscript 𝛽 𝑝 {\displaystyle{\displaystyle\beta_{p}}} : β p
  • γ p subscript 𝛾 𝑝 {\displaystyle{\displaystyle\gamma_{p}}} : γ p
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