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Formula:8965

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Digital Library of Mathematical Functions ID 28.8.E7

S ^ m ∼ ( π ⁢ h 2 ⁢ ( m ! ) 2 ) 1 / 4 ⁢ ( 1 - 2 ⁢ m + 1 8 ⁢ h + m 4 + 2 ⁢ m 3 - 121 ⁢ m 2 - 122 ⁢ m - 84 2048 ⁢ h 2 + ⋯ ) - 1 / 2 . asymptotic-expansion subscript ^ 𝑆 𝑚 superscript 𝜋 ℎ 2 superscript 𝑚 2 1 4 superscript 1 2 𝑚 1 8 ℎ superscript 𝑚 4 2 superscript 𝑚 3 121 superscript 𝑚 2 122 𝑚 84 2048 superscript ℎ 2 ⋯ 1 2 {\displaystyle{\displaystyle\widehat{S}_{m}\sim\left(\frac{\pi h}{2(m!)^{2}}% \right)^{\ifrac{1}{4}}\left(1-\frac{2m+1}{8h}+\dfrac{m^{4}+2m^{3}-121m^{2}-122% m-84}{2048h^{2}}+\cdots\right)^{-\ifrac{1}{2}}.}}


Constraint(s)

Symbols List

  • ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}} :
  • π {\displaystyle{\displaystyle\pi}} : the ratio of the circumference of a circle to its diameter
  • ! {\displaystyle{\displaystyle!}} :
  • m 𝑚 {\displaystyle{\displaystyle m}} : integer
  • h ℎ {\displaystyle{\displaystyle h}} : parameter
  •  Edit this on Wikidata

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This page was last edited on 28 January 2024, at 10:30.
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