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Formula:3215

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Digital Library of Mathematical Functions ID 8.6.E3

γ ⁡ ( a , z ) = z a ⁢ ∫ 0 ∞ exp ⁡ ( - a ⁢ t - z ⁢ e - t ) ⁢ d t , incomplete-gamma 𝑎 𝑧 superscript 𝑧 𝑎 superscript subscript 0 𝑎 𝑡 𝑧 superscript 𝑒 𝑡 𝑡 {\displaystyle{\displaystyle\gamma\left(a,z\right)=z^{a}\int_{0}^{\infty}\exp% \left(-at-ze^{-t}\right)\mathrm{d}t,}}


Constraint(s)

ℜ ⁡ a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}

Symbols List

  • d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}} : differential of x
  • exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}} : exponential function
  • e {\displaystyle{\displaystyle\mathrm{e}}} : base of natural logarithm
  • γ ⁡ ( a , z ) incomplete-gamma 𝑎 𝑧 {\displaystyle{\displaystyle\gamma\left(\NVar{a},\NVar{z}\right)}} : incomplete gamma function
  • ∫ {\displaystyle{\displaystyle\int}} : integral
  • ℜ ⁡ absent {\displaystyle{\displaystyle\Re}} : real part
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex variable
  • a 𝑎 {\displaystyle{\displaystyle a}} : parameter
  •  Edit this on Wikidata

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This page was last edited on 3 March 2024, at 01:54.
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