Formula:2625

Digital Library of Mathematical Functions ID 5.6.E5

${\displaystyle{\displaystyle\exp\left((1-s)\psi\left(x+s^{1/2}\right)\right)\leq\frac{\Gamma\left(x+1\right)}{\Gamma\left(x+s\right)}\leq\exp\left((1-s)\psi\left(x+\tfrac{1}{2}(s+1)\right)\right),}}$

Constraint(s)

${\displaystyle{\displaystyle 0<s<1}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}$: psi (or digamma) function
• ${\displaystyle{\displaystyle\exp\NVar{z}}}$: exponential function
• ${\displaystyle{\displaystyle s}}$: real or complex variable
• ${\displaystyle{\displaystyle x}}$: real variable
 

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