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Asymptotic and exact series representations for the incomplete Gamma function [PDF]

, 2005
Using a variational approach, two new series representations for the incomplete Gamma function are derived: the first is an asymptotic series, which contains and improves over the standard asymptotic expansion; the second is a uniformly convergent series,
Abramowitz M., Amore P., Amore P., Arteca G. A., Gautschi W., Kleinert H., P Amore   +6 more
core   +2 more sources

Monotonicity and inequalities involving the incomplete gamma function

Journal of Inequalities and Applications, 2016
In the article, we deal with the monotonicity of the function x → [ ( x p + a ) 1 / p − x ] / I p ( x ) $x\rightarrow[ (x^{p}+a )^{1/p}-x]/I_{p}(x)$ on the interval ( 0 , ∞ ) $(0, \infty)$ for p > 1 $p>1$ and a > 0 $a>0$ , and present the necessary and ...
Zhen-Hang Yang, Wen Zhang, Yu-Ming Chu
doaj   +1 more source

A Series Representation for the Hurwitz–Lerch Zeta Function

Axioms, 2021
We derive a new formula for the Hurwitz–Lerch zeta function in terms of the infinite sum of the incomplete gamma function. Special cases are derived in terms of fundamental constants.
Robert Reynolds, Allan Stauffer
doaj   +1 more source

Distribution and probability of rainfall occurrence in Cáceres, Mato Grosso state, Brazil

Pesquisa Agropecuária Tropical, 2012
Rainfall is an important meteorological element, and the knowledge on its historical records is relevant for monitoring the impacts caused by its prolonged excess or lack.
Jaqueline Aguilla Pizzato, Rivanildo Dallacort, Rafael César Tieppo, Alcir José Modolo, Cassiano Cremon, Patrícia Simone Palhana Moreira   +5 more
doaj   +1 more source

Definite Integral of Logarithmic Functions in Terms of the Incomplete Gamma Function

Mathematics, 2021
In this article we derive some entries and errata for the book of Gradshteyn and Ryzhik which were originally published by Bierens de Haan. We summarize our results using tables for easy reading and referencing.
Robert Reynolds, Allan Stauffer
doaj   +1 more source

Actuarial values calculated using the incomplete Gamma function

Statistica, 2013
The complete expectation-of-life for a person and the actuarial present value of continuous life annuities are defined by integrals. In all of them at least one of the factors is a survival function value ratio. If de Moivre’s law of mortality is chosen,
Giovanni Mingari Scarpello, Daniele Ritelli, Dario Spelta   +2 more
doaj   +1 more source

Extension of the Sophomore’s Dream

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021
In this article, we are going to look at the convergence properties of the integral ∫01(ax+b)cx+ddx\int_0^1 {{{\left( {ax + b} \right)}^{cx + d}}dx}, and express it in series form, where a, b, c and d are real parameters.
Román Gábor
doaj   +1 more source

Infinite Sum of the Incomplete Gamma Function Expressed in Terms of the Hurwitz Zeta Function

Mathematics, 2021
We apply our simultaneous contour integral method to an infinite sum in Prudnikov et al. and use it to derive the infinite sum of the Incomplete gamma function in terms of the Hurwitz zeta function.
Robert Reynolds, Allan Stauffer
doaj   +1 more source

Environmental and genetic effects on the lactation curves of four genetic groups of crossbred Holstein-Zebu cows

Revista Brasileira de Zootecnia, 2012
The objective of this study was to evaluate the effects of genetic group and environmental factors, including farm of origin, season of calving and lactation number, on the individual lactation curves of 1,010 Holstein-Gyr, Guzerat-Holstein, Holstein ...
Joana Ribeiro da Glória, José Aurélio Garcia Bergmann, Célia Raquel Quirino, José Reinaldo Mendes Ruas, Jonas Carlos Campos Pereira, Ronaldo Braga Reis, Sandra Gesteira Coelho, Martinho de Almeida e Silva   +7 more
doaj   +1 more source

Inverse Generalized Gamma Distribution with it's properties [PDF]

المجلة العراقية للعلوم الاحصائية, 2020
: In this paper, we introduce a new life time distribution . This distribution based on the reciprocal of Generalized Gamma (GG) random variable . This new distribution is called the Inverse Generalized Gamma (IGG) Distribution in which some of the ...
Hayfa Abdul Jawad Saieed, Mehasen Saleh Abdulla, Heyam Abd Al- majeed Hayawi   +2 more
doaj   +1 more source