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Formula:3289

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Digital Library of Mathematical Functions ID 8.11.E18

S n ⁢ ( x ) ∼ ∑ k = 0 ∞ d k ⁢ ( x ) ⁢ n - k , asymptotic-expansion subscript 𝑆 𝑛 𝑥 superscript subscript 𝑘 0 subscript 𝑑 𝑘 𝑥 superscript 𝑛 𝑘 {\displaystyle{\displaystyle S_{n}(x)\sim\sum_{k=0}^{\infty}d_{k}(x)n^{-k},}}


Constraint(s)

n → ∞ → 𝑛 {\displaystyle{\displaystyle n\to\infty}}

Symbols List

  • ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}} :
  • x 𝑥 {\displaystyle{\displaystyle x}} : real variable
  • k 𝑘 {\displaystyle{\displaystyle k}} : nonnegative integer
  • n 𝑛 {\displaystyle{\displaystyle n}} : nonnegative integer
  • S n ⁢ ( x ) subscript 𝑆 𝑛 𝑥 {\displaystyle{\displaystyle S_{n}(x)}} : function (locally)
  • d k ⁢ ( x ) subscript 𝑑 𝑘 𝑥 {\displaystyle{\displaystyle d_{k}(x)}} : coefficients
  •  Edit this on Wikidata

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