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Otolith Deterioration: Factors Affecting Microvascular and Structural Integrity. [PDF]
Choi EH +6 more
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Preoperative nutritional risk and adverse perioperative outcomes in children with congenital choledochal cysts: a retrospective cohort study. [PDF]
Liu X +10 more
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Wernicke Encephalopathy Complicating a Distinctive POLG Phenotype With MNGIE-Like Features. [PDF]
Capece G +13 more
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Sleep-Dependent Clearance of Brain Metabolites via the Glymphatic System: Implications for Alzheimer's Pathophysiology. [PDF]
Zare F +6 more
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From dog bite to dialysis: complement-mediated haemolytic uraemic syndrome . [PDF]
Fredriksen TE, Mian BU, Dolgos S.
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Inequalities and Bounds for the Incomplete Gamma Function
Results in Mathematics, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Edward Neuman
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On Defining The Incomplete Gamma Function
Integral Transforms and Special Functions, 2003The incomplete Gamma function $\gamma \lpar \alpha\comma \; x_+\rpar $ is defined as locally summable function on the real line for $\alpha \gt 0$ by $$\gamma \lpar \alpha\comma \; x_+\rpar =\vint_0^{x_+} u^{\alpha -1} e^{-u}\, \hbox{d}u\comma$$ the integral diverging for $\alpha\leq 0$ .
Adem Kiliçman
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The incomplete gamma functions
The Mathematical Gazette, 2016Summary: Recall the integral definition of the gamma function: \(\Gamma(a)=\int_0^{\infty}t^{a-1}e^{-t}dt\) for \(a>0\). By splitting this integral at a point \(x\geq 0\), we obtain the two \textit{incomplete gamma functions}: \[ \gamma(a,x)=\int_0^xt^{a-1}e^{-t}dt,\eqno{(1)} \] \[ \Gamma(a,x)=\int_x^{\infty}t^{a-1}e^{-t}dt\eqno{(2)} \] \(\Gamma(a,x)\)
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