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Formula:10128

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Digital Library of Mathematical Functions ID 32.11.E1

w ⁢ ( x ) = - 1 6 ⁢ | x | + d ⁢ | x | - 1 / 8 ⁢ sin ⁡ ( ϕ ⁢ ( x ) - θ 0 ) + o ⁡ ( | x | - 1 / 8 ) , 𝑤 𝑥 1 6 𝑥 𝑑 superscript 𝑥 1 8 italic-ϕ 𝑥 subscript 𝜃 0 little-o superscript 𝑥 1 8 {\displaystyle{\displaystyle w(x)=-\sqrt{\tfrac{1}{6}|x|}+d|x|^{-1/8}\sin\left% (\phi(x)-\theta_{0}\right)+o\left(|x|^{-1/8}\right),}}


Constraint(s)

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

Symbols List

  • o ⁡ ( x ) little-o 𝑥 {\displaystyle{\displaystyle o\left(\NVar{x}\right)}} : order less than
  • sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}} : sine function
  • x 𝑥 {\displaystyle{\displaystyle x}} : real
  • ϕ ⁢ ( z ) italic-ϕ 𝑧 {\displaystyle{\displaystyle\phi(z)}} : function
  • d 𝑑 {\displaystyle{\displaystyle d}} : constant
  • θ 0 subscript 𝜃 0 {\displaystyle{\displaystyle\theta_{0}}} : constant
  •  Edit this on Wikidata

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