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Formula:10140

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Digital Library of Mathematical Functions ID 32.11.E13

w ⁢ ( x ) = d ⁢ | x | - 1 / 4 ⁢ sin ⁡ ( ϕ ⁢ ( x ) - χ ) + O ⁡ ( | x | - 5 / 4 ⁢ ln ⁡ | x | ) , 𝑤 𝑥 𝑑 superscript 𝑥 1 4 italic-ϕ 𝑥 𝜒 Big-O superscript 𝑥 5 4 𝑥 {\displaystyle{\displaystyle w(x)=d|x|^{-1/4}\sin\left(\phi(x)-\chi\right)+O% \left(|x|^{-5/4}\ln|x|\right),}}


Constraint(s)

x → - ∞ → 𝑥 {\displaystyle{\displaystyle x\to-\infty}}

Symbols List

  • O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}} : order not exceeding
  • ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}} : principal branch of logarithm function
  • sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}} : sine function
  • x 𝑥 {\displaystyle{\displaystyle x}} : real
  • χ 𝜒 {\displaystyle{\displaystyle\chi}} : constant
  • ϕ ⁢ ( z ) italic-ϕ 𝑧 {\displaystyle{\displaystyle\phi(z)}} : function
  • d 𝑑 {\displaystyle{\displaystyle d}} : constant
  •  Edit this on Wikidata

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