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Formula:3301

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Digital Library of Mathematical Functions ID 8.12.E8

T ⁢ ( a , η ) ∼ e 1 2 ⁢ a ⁢ η 2 2 ⁢ π ⁢ a ⁢ ∑ k = 0 ∞ c k ⁢ ( η ) ⁢ ( - a ) - k , asymptotic-expansion 𝑇 𝑎 𝜂 superscript 𝑒 1 2 𝑎 superscript 𝜂 2 2 𝜋 𝑎 superscript subscript 𝑘 0 subscript 𝑐 𝑘 𝜂 superscript 𝑎 𝑘 {\displaystyle{\displaystyle T(a,\eta)\sim\frac{e^{\frac{1}{2}a\eta^{2}}}{% \sqrt{2\pi a}}\sum_{k=0}^{\infty}c_{k}(\eta)(-a)^{-k},}}


Constraint(s)

Symbols List

  • ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}} :
  • π {\displaystyle{\displaystyle\pi}} : the ratio of the circumference of a circle to its diameter
  • e {\displaystyle{\displaystyle\mathrm{e}}} : base of natural logarithm
  • a 𝑎 {\displaystyle{\displaystyle a}} : parameter
  • k 𝑘 {\displaystyle{\displaystyle k}} : nonnegative integer
  • η ⁢ ( λ ) 𝜂 𝜆 {\displaystyle{\displaystyle\eta(\lambda)}} : η ( λ )
  • T ⁢ ( a , η ) 𝑇 𝑎 𝜂 {\displaystyle{\displaystyle T(a,\eta)}} : function
  • c k ⁢ ( η ) subscript 𝑐 𝑘 𝜂 {\displaystyle{\displaystyle c_{k}(\eta)}} : coefficients
  •  Edit this on Wikidata

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