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Formula:3265

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Digital Library of Mathematical Functions ID 8.10.E10

x 2 ⁢ a ⁢ ( ( 1 + 2 x ) a - 1 ) < x 1 - a ⁢ e x ⁢ Γ ⁡ ( a , x ) ≤ x a ⁢ c a ⁢ ( ( 1 + c a x ) a - 1 ) , 𝑥 2 𝑎 superscript 1 2 𝑥 𝑎 1 superscript 𝑥 1 𝑎 superscript 𝑒 𝑥 incomplete-Gamma 𝑎 𝑥 𝑥 𝑎 subscript 𝑐 𝑎 superscript 1 subscript 𝑐 𝑎 𝑥 𝑎 1 {\displaystyle{\displaystyle\frac{x}{2a}\left(\left(1+\frac{2}{x}\right)^{a}-1% \right)<x^{1-a}e^{x}\Gamma\left(a,x\right)\leq\frac{x}{ac_{a}}\left(\left(1+% \frac{c_{a}}{x}\right)^{a}-1\right),}}


Constraint(s)

0 < a < 1 0 𝑎 1 {\displaystyle{\displaystyle 0<a<1}}

Symbols List

  • 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
  • x 𝑥 {\displaystyle{\displaystyle x}} : real variable
  • a 𝑎 {\displaystyle{\displaystyle a}} : parameter
  • c a subscript 𝑐 𝑎 {\displaystyle{\displaystyle c_{a}}} : coefficients
  •  Edit this on Wikidata

Resources that cite this formula

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This page was last edited on 3 March 2024, at 01:49.
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