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On a Class of Integrals Appearing in Hadron Scattering and the Fox’s H-Function
Current Issue
Volume 2, 2014
Issue 1 (February)
Pages: 1-4   |   Vol. 2, No. 1, February 2014   |   Follow on         
Paper in PDF Downloads: 24   Since Aug. 28, 2015 Views: 1527   Since Aug. 28, 2015
Authors
[1]
E. A. Notte Cuello , Dpto de Matematicas, Facultadde Ciencias, Universidad de La Serena, La Serena, Chile; Instituto de Matemática, Universidade Estadual de Campinas, Campinas, Brazil.
[2]
M. J. Menon , Instituto de Física Gleb Wataghin, Universidade Estadual de Campinas, Campinas, Brazil.
[3]
E. Capelasde Oliveira , Dpto de Matematicas, Facultadde Ciencias, Universidad de La Serena, La Serena, Chile.
Abstract
In the study of empirical determinations of the eikonal function from hadron-hadron elastic scattering data, a class on integrals cannot be represented in a general closed form. Some particular cases can be written in terms of a Bessel function, only. In this paper, using the Mellin-Barnes integrals we obtain a general integral representation that can be identifying to the Fox's H-function, which is related to that class of integrals. Some particular cases are discussed.
Keywords
Fox's H-Function, Mellin-Barnes Integral, Integral Transform, Hadron Scattering
Reference
[1]
H. M. Fried, Basics of Functional Methods and Eikonal Models, Editions Frontieres, Gif-sur-Yvette, (1990).
[2]
V. Barone and E. Predazzi, High-Energy Particle Diffraction, Springer-Verlag, Berlin, (2002).
[3]
R. F. Avila and M. J. Menon, Eikonal zeros in the momentum transfer space from proton-proton scattering: an empirical analysis, Eur. Phys. J., C 54, 555-576, (2008).
[4]
D. A. Fagundes and M. J. Menon, Applicability of a representation for the Martins's real-part formula in model-independent analysis, Int. J. Mod. Phys. A, 26, 3219 (2011).
[5]
D. A. Fagundes, M. J. Menon, G. L. P. Silva, Model-independent data reductions of elastic proton-proton scattering, Eur. Phys. J. C, 71, 1637 (2011).
[6]
G. L. P. Silva, M. J. Menon and R. F. Avila, Proton profile at 52.8 GeV, Int. J. Mod. Phys. E 16, 2923-2926 (2007).
[7]
R. F. Avila, S. D. Campos, M. J. Menon, and J. Montanha, Phenomenological analysis connecting proton-proton and antiproton-proton elastic scattering, Eur. Phys. J., 47, 171-186, (2006).
[8]
P. A. S. Carvalho, A. F. Martini, and M. J. Menon, Eikonal representation in the momentum-transfer space, Eur. Phys. J. C 39, 359-376, (2005).
[9]
P. A. S. Carvalho and M. J. Menon, Evidence for eikonal zeros in the momentum-transfer space, Phys. Rev. D 56, 7321-7324, (1997).
[10]
R. Figueiredo Camargo, R. Charnet, and E. Capelas de Oliveira, On some fractional Green's functions, J. Math. Phys., 50, 043514 (2009).
[11]
R. Figueiredo Camargo, Ary O. Chiacchio, R. Charnet, and E. Capelas de Oliveira, Solution of the fractional Langevinequation and the Mittag-Leffler functions, J. Math. Phys., 50, 063507 (2009).
[12]
R. Figueiredo Camargo, E. Capelas de Oliveira, and J. Vaz Jr., On anomalous diffusion and the fractional generalized Langevin equation for a harmonic oscillator, J. Math. Phys., 50, 123518 (2009).
[13]
E. Capelas de Oliveira, F. Silva Costa and J. Vaz Jr., The fractional Schrödinger equation for delta potentials, J. Math. Phys. 51, 123517 (2010).
[14]
E. Capelas de Oliveira and J. Vaz Jr., Tunneling in fractional quantum mechanics, J. Physics A: Math. andTheor., 44, 185303 (2011).
[15]
R. Figueiredo Camargo, E. Capelas de Oliveira and J. Vaz Jr., On the generalized Mittag-Leffler function and its application in a fractional telegraph equation, Math. Phys. Anal. Geom., 15, 1-16, (2012).
[16]
R. Figueiredo Camargo, E. Capelas de Oliveira and J. Vaz Jr., On the generalized Mittag-Leffler function and its application in a fractional telegraph equation, Math. Phys. Anal. Geom., 15, 1-16, (2012).
[17]
A. P. Prudnikov, Yu. A. Brychkov and O. I. Marichev, Integrals and Series, Gordon and Breach Science Publishers, New York, (1992).
[18]
I. S. Gradshteyn and I. M. Ryzhik, Table of integrals, series, and produts, edited by A. Jeffrey and D. Zwllinger, Seventh Edition, Associated Press, New York, (2007).
[19]
A. M. Mathai, R. S. Saxena and H. J. Haubold, The H-function, Theory and Application, Springer, New York, (2010).
[20]
F. Silva Costa, Fox's H-Function and Applications, (in Portuguese), PhD Thesis, Campinas, (2011).
[21]
T. R. Prabhakar, A singular integral equation with a generalized Mittag-Leffler function in the kernel, Yokohama Math. J., 19, 7-15, (1971).
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