Algunas representaciones simples de la función hipergeométrica generalizada 2R1 (a, b; c; τ ; x)
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Keywords
generalized hypergeometric function, simple representations.
Abstract
The field of especial functions have had a remarkable development during the last deacades because there are many phenomena that can be studied through ont the use of these functions themselves, such as related stochastics processes, operational research, queuing theory, functional equations, vibrations of plates, heat conduction, elasticity, and radiation. Along this paper work, an extension of the theories presented by M. Dotsenko en 1991 is considered. M. Dotsenko introduced the generalization of the hypergeometric function of Gauss referred as 2Rτ1 (z), and he established it 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. Along this paper work some simple representations of the function 2R1(a, b; c; τ ; z) are displayed, which will be very useful for future researchers since they permit simplify calculus at the time of solving problems involving this function.
MSC: 33D15, 33D90, 33D60, 34M03, 62E15
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References
[2] J. B. Slater. Generalized hypergeometric functions. University Press, Cambridge, 1966.
[3] H. M. Srivastava and P. W. Karlsson. Multiple gaussian hypergeometric series. John Wiley & Sons, New York, 1985.
[4] H. M. Srivastava, K. C. Gupta and S. P. Goyal. The H-functions of one and two variables. South Asian Publishers, New Delhi, 1982.
[5] E. M. Wright. The asymptotic expansion of the generalized hypergeometric function. J. London Math. Soc. 10, 286–293, 1935.
[6] E. M. Wright. The asymptotic expansion of the generalized hypergeometric function. Proc. London Math. Soc. 2(46), 389–408 (1940).
[7] L. Galu´e, A. Al-Zamel and S. L. Kalla. Further results on generalized hypergeometricfunctions. Applied Mathematics and Computation, 136, 17–25 (2003).
[8] N. N. Levedev. Special functions and their applications Prentice-Hall Inc., New York, 1965.
[9] M. Dotsenko. On some applications of Wrigt’s hypergeometric functions. C. R. Acad. Bulgare Sci, 44, 13–16 (1991).
[10] N. Virchenko. On some generalizations of the functions of hypergeometric type. Fractional Calculus and Applied Analysis, 2(3), 233–244 (1999).
[11] A. P. Prudnikov, Yu. A. Brychkov and O. I. Marichev. Integrals and series. Gordon and Breach Science Publishers, 3, New York, 1992.
[12] J. B. Seaborn. Hypergeometric functions an their applications. Springer-Verlag, New york, 1991.
[13] J. Castillo y R. Bertel. Algunas integrales indefinidas que contienen a la función hipergeom´etrica generalizada. Centro de investigaciones de la Universidad de la Guajira, 2004.
[14] F. Al-Musallam and S. L. Kalla. Further results on a generalized gamma function occuring in diffraction theory. Integral Transform. Espec. Funct, 7, 175–190 (1998).
[15] N. Virchenko, S. L. Kalla and A. Al-Zamel. Some results on a generalized hypergeometricfunction. Integral Transforms and Special Function, 12(1), 89–100 (2001).