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Formula:762

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Digital Library of Mathematical Functions ID 2.5.E16

I ⁢ ( x ) = ∑ s = 0 n - 1 ( c s ⁢ ln ⁡ x + d s ) ⁢ x - 2 ⁢ s - 1 + O ⁡ ( x - 2 ⁢ n - 1 + ϵ ) , 𝐼 𝑥 superscript subscript 𝑠 0 𝑛 1 subscript 𝑐 𝑠 𝑥 subscript 𝑑 𝑠 superscript 𝑥 2 𝑠 1 Big-O superscript 𝑥 2 𝑛 1 italic-ϵ {\displaystyle{\displaystyle I(x)=\sum_{s=0}^{n-1}(c_{s}\ln x+d_{s})x^{-2s-1}+% O\left(x^{-2n-1+\epsilon}\right),}}


Constraint(s)

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
  • ϵ italic-ϵ {\displaystyle{\displaystyle\epsilon}} : parameter
  • c 𝑐 {\displaystyle{\displaystyle c}} : point
  • I ⁢ ( x ) 𝐼 𝑥 {\displaystyle{\displaystyle I(x)}} : convolution integral
  • d 𝑑 {\displaystyle{\displaystyle d}} : point
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