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In this paper we present a family of Pearson's discrete distributions which are generated by the hypergeometric function p+1Fp, an univariate extension of the Gaussian hypergeometric function. It allows us to generalize the study of this type of distributions, whatever the order of the hypergeometric function which is considered. We study the properties that they present, like a recurrence relation that the moments verify, from which we can use the moment's method to estimate the parameters. Also we have obtained a summation result through which we can calculate the probability mass function and the moments of a wide class of distributions. [ABSTRACT FROM AUTHOR]

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 2Rr1 (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 Galué 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; r; 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. [ABSTRACT FROM AUTHOR]