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Formula:2834

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Digital Library of Mathematical Functions ID 5.11.E14

Γ ⁡ ( z + a ) Γ ⁡ ( z + b ) ∼ ( z + a + b - 1 2 ) a - b ⁢ ∑ k = 0 ∞ H k ⁢ ( a , b ) ( z + 1 2 ⁢ ( a + b - 1 ) ) 2 ⁢ k . asymptotic-expansion Euler-Gamma 𝑧 𝑎 Euler-Gamma 𝑧 𝑏 superscript 𝑧 𝑎 𝑏 1 2 𝑎 𝑏 superscript subscript 𝑘 0 subscript 𝐻 𝑘 𝑎 𝑏 superscript 𝑧 1 2 𝑎 𝑏 1 2 𝑘 {\displaystyle{\displaystyle\frac{\Gamma\left(z+a\right)}{\Gamma\left(z+b% \right)}\sim\left(z+\frac{a+b-1}{2}\right)^{a-b}\sum_{k=0}^{\infty}\frac{H_{k}% (a,b)}{\left(z+\tfrac{1}{2}(a+b-1)\right)^{2k}}.}}


Constraint(s)

Symbols List

  • Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}} : gamma function
  • ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}} :
  • ℜ ⁡ absent {\displaystyle{\displaystyle\Re}} : real part
  • 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
  • H k ⁢ ( a , b ) subscript 𝐻 𝑘 𝑎 𝑏 {\displaystyle{\displaystyle H_{k}(a,b)}} : coefficients (locally)
  •  Edit this on Wikidata

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