Some improper integrals with integration infinity limit involving generalizad hypergeometric function 2R1(a, b; c; τ ; z)
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Keywords
generalized hypergeometric function, improper integrals.
Abstract
In 1991 M. Dotsenko presented a generalization of Gauss’ hypergeometric function refered as 2Rτ1(z), and established its representation in series and integral. It is important to remark that in 1999 Nina Virchenko and, later in 2003, Leda Galu´e considered this function by introducing a set of recurrence and differentiation formulas; they permit simplify some complicated calculus. Kalla et al estudied this function and they presented a new unified form of the gamma function. Later in 2006, Castillo et al present some simple representation for this function. Along this paper work some improper integrals with integration infinity limit involving generalized hypergeometric function
2R1(a, b; c; τ ; z) are displayed.
MSC: 33D15, 33D90, 33D60, 34M03, 62E15
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References
[2] A. M. Mathai and R. K. Saxena. Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences, ISBN 0–387–06482–6. New york: Springer-Verlag, 1970.
[3] N. N. Levedev. Special functions and their applications, ISBN 0–486–60624–4. New York: Prentice-Hall, 1965.
[4] N. Virchenko. On some generalizations of the functions of hypergeometric type. Fractional Calculus and Applied Analysis, ISSN 1311–0454, 2(3), 233–244 (1999).
[5] J. Castillo y C. Jiménez. Algunas representaciones simples de la función hipergeométrica generalizada. Ingeniería y Ciencia, ISSN 1794–9165, 2(4), 75–94 (2006).
[6] Earl David Rainville. Special Functions, ISBN 0–8284–0258–2. New York: Chelsea Publishing Company, 1960.
[7] A. P. Prudnikov, Yu. A. Brychkov and O. I. Marichev. Integrals and Series: More Special Functions , ISBN 2–88124–682–6. New York: Gordon and Breach Science Publishers, 3, 1992.
[8] George E. Andrews, Richard Askey and Ranjan Roy. Special Functions, ISBN 0–521–62321–9. New York: Cambridge University Press 1999.
[9] Ben Nakhi and S. L. Kalla. A generalized beta functions and associated probability density. International Journal of Mathematics and Mathematics Sciences, ISSN 0161–1712, 30, 467–478 (2002).
[10] A. M. Mathai and R. K. Saxena. Generalized Hypergeometric Functions with Applications in Statistics and Physical Sciences. New York: Springer Verlag, ISBN 0–470–26380–6, 1973