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Formula:802

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Digital Library of Mathematical Functions ID 2.6.E7

S ⁢ ( x ) ∼ 2 ⁢ π 3 ⁢ ∑ s = 0 ∞ ( - 1 ) s ⁢ ( - 1 3 s ) ⁢ x - s - ( 1 / 3 ) - ∑ s = 1 ∞ 3 s ⁢ ( s - 1 ) ! 2 ⋅ 5 ⁢ ⋯ ⁢ ( 3 ⁢ s - 1 ) ⁢ x - s ; asymptotic-expansion 𝑆 𝑥 2 𝜋 3 superscript subscript 𝑠 0 superscript 1 𝑠 binomial 1 3 𝑠 superscript 𝑥 𝑠 1 3 superscript subscript 𝑠 1 superscript 3 𝑠 𝑠 1 ⋅ 2 5 ⋯ 3 𝑠 1 superscript 𝑥 𝑠 {\displaystyle{\displaystyle S(x)\sim\frac{2\pi}{\sqrt{3}}\sum_{s=0}^{\infty}(% -1)^{s}{\genfrac{(}{)}{0.0pt}{}{-\frac{1}{3}}{s}}x^{-s-(1/3)}-\sum_{s=1}^{% \infty}\frac{3^{s}(s-1)!}{2\cdot 5\cdots(3s-1)}x^{-s};}}


Constraint(s)

Symbols List

  • ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}} :
  • ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}} :
  • π {\displaystyle{\displaystyle\pi}} : the ratio of the circumference of a circle to its diameter
  • ! {\displaystyle{\displaystyle!}} :
  • S ⁢ ( x ) 𝑆 𝑥 {\displaystyle{\displaystyle S(x)}} : integral
  •  Edit this on Wikidata

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This page was last edited on 28 January 2024, at 10:02.
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