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Formula:835

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Digital Library of Mathematical Functions ID 2.6.E39

t μ - 1 ∗ t - s - α = Γ ⁡ ( μ ) ⁢ Γ ⁡ ( 1 - s - α ) Γ ⁡ ( μ + 1 - s - α ) ⁢ t μ - s - α , ∗ superscript 𝑡 𝜇 1 superscript 𝑡 𝑠 𝛼 Euler-Gamma 𝜇 Euler-Gamma 1 𝑠 𝛼 Euler-Gamma 𝜇 1 𝑠 𝛼 superscript 𝑡 𝜇 𝑠 𝛼 {\displaystyle{\displaystyle t^{\mu-1}\ast t^{-s-\alpha}=\frac{\Gamma\left(\mu% \right)\Gamma\left(1-s-\alpha\right)}{\Gamma\left(\mu+1-s-\alpha\right)}t^{\mu% -s-\alpha},}}


Constraint(s)

t > 0 𝑡 0 {\displaystyle{\displaystyle t>0}}

Symbols List

  • Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}} : gamma function
  • μ 𝜇 {\displaystyle{\displaystyle\mu}} : order
  • ∗ ∗ {\displaystyle{\displaystyle\ast}} : convolution (locally)
  •  Edit this on Wikidata

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