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Formula:3315

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Digital Library of Mathematical Functions ID 8.12.E15

Q ⁡ ( a , a ) ∼ 1 2 + 1 2 ⁢ π ⁢ a ⁢ ∑ k = 0 ∞ c k ⁢ ( 0 ) ⁢ a - k , asymptotic-expansion incomplete-gamma-Q 𝑎 𝑎 1 2 1 2 𝜋 𝑎 superscript subscript 𝑘 0 subscript 𝑐 𝑘 0 superscript 𝑎 𝑘 {\displaystyle{\displaystyle Q\left(a,a\right)\sim\frac{1}{2}+\frac{1}{\sqrt{2% \pi a}}\sum_{k=0}^{\infty}c_{k}(0)a^{-k},}}


Constraint(s)

| ph ⁡ a | ≤ π - δ phase 𝑎 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}a|\leq\pi-\delta}}

Symbols List

  • ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}} :
  • π {\displaystyle{\displaystyle\pi}} : the ratio of the circumference of a circle to its diameter
  • Q ⁡ ( a , z ) incomplete-gamma-Q 𝑎 𝑧 {\displaystyle{\displaystyle Q\left(\NVar{a},\NVar{z}\right)}} : normalized incomplete gamma function
  • ph phase {\displaystyle{\displaystyle\operatorname{ph}}} : phase
  • a 𝑎 {\displaystyle{\displaystyle a}} : parameter
  • k 𝑘 {\displaystyle{\displaystyle k}} : nonnegative integer
  • δ 𝛿 {\displaystyle{\displaystyle\delta}} : small positive constant
  • c k ⁢ ( η ) subscript 𝑐 𝑘 𝜂 {\displaystyle{\displaystyle c_{k}(\eta)}} : coefficients
  •  Edit this on Wikidata

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