The Gamma Function: basic properties and some applications

Authors

  • Maruja Gavilán Gonzales Departamento de Matemáticas, UNMSM
  • Martha Gonzales Bohorquez Departamento de Matemáticas, UNMSM

DOI:

https://doi.org/10.17268/sel.mat.2017.02.05

Keywords:

Lebesgue Integral, Gamma Function, Beta Function, Convolution, Continuous Distribution

Abstract

The goal of the present work is to study some properties and applications of the Gamma Function, denoted by Γ. Initially, we use the Lebesgue Integral Theory in order to prove that the improper integral given by Γ is convergent. We describe the extended domain property of Γ, and we also deduce some elementary properties. We present two different ways of proving that B(x, y) = Γ(x)Γ(y)/Γ(x+y) , where B is the Beta Function. Finally, we include some applications of the Gamma Function, between them some serve up as tools on Reliability Engineering.

References

E. ARTIN, The Gamma function. Translated by M. Butler, Holt. Rinehart and Winston, New York, 1964.

TOM M. APOSTOL, Análisis matemático. Reverte, Barcelona, 1996.

DEPOOL RIVERO, RAMON & DIÓSCORO, MONASTERIO, Probabilidad y Estadística. Aplicaciones a la Ingeniería. Universidad Nacional Experimental Politécnica “Antonio José de Sucre”. Barquisimeto. Venezuela. 2013. http://bqto.unexpo.edu.ve/avisos/PROBABILIDADYESTADISTICA(2-7-13).pdf (visitado 10-10-2016).

NORBERTO FAVA & FELIPE ZÓ, Medida e Integral de Lebesgue, Departamento de Matemática, FCEyN, Universidad de Buenos Aires. Argentina. 2013. http://cms.dm.uba.ar/depto/public/Cursodegrado/fascgrado4.pdfhttp://cms.dm.uba.ar/depto/public/Cursodegrado/fascgrado4.pdf (visitado 10-10-2016).

MAURICE GODEFROY, La fonction Gamma; Théorie, Histoire, Bibliographie, Gauthier-Villars, Paris, 1901.

PEREZ A. JUAN & C. SERRAT, Distribuciones habituales en fiabilidad.UPC,Catalunya.2006http://www.uoc.edu/in3/emath/docs/Q1P

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Published

2017-12-15

How to Cite

Gavilán Gonzales, M., & Gonzales Bohorquez, M. (2017). The Gamma Function: basic properties and some applications. Selecciones Matemáticas, 4(02), 177-191. https://doi.org/10.17268/sel.mat.2017.02.05

Issue

Vol. 4 No. 02 (2017): August - December

Section

Articles

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