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Formula:2833

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Digital Library of Mathematical Functions ID 5.11.E13

Γ ⁡ ( z + a ) Γ ⁡ ( z + b ) ∼ z a - b ⁢ ∑ k = 0 ∞ G k ⁢ ( a , b ) z k , asymptotic-expansion Euler-Gamma 𝑧 𝑎 Euler-Gamma 𝑧 𝑏 superscript 𝑧 𝑎 𝑏 superscript subscript 𝑘 0 subscript 𝐺 𝑘 𝑎 𝑏 superscript 𝑧 𝑘 {\displaystyle{\displaystyle\frac{\Gamma\left(z+a\right)}{\Gamma\left(z+b% \right)}\sim z^{a-b}\sum_{k=0}^{\infty}\frac{G_{k}(a,b)}{z^{k}},}}


Constraint(s)

Symbols List

  • Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}} : gamma function
  • ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}} :
  • k 𝑘 {\displaystyle{\displaystyle k}} : nonnegative integer
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex variable
  • a 𝑎 {\displaystyle{\displaystyle a}} : real or complex variable
  • b 𝑏 {\displaystyle{\displaystyle b}} : real or complex variable
  • G k ⁢ ( a , b ) subscript 𝐺 𝑘 𝑎 𝑏 {\displaystyle{\displaystyle G_{k}(a,b)}} : coefficients (locally)
  •  Edit this on Wikidata

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