Search

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]

In this paper we show the presence of the phenomena of approximation organized by a definition of limit in the cases of the successions of real numbers and the real functions of one real variable. The exposition includes the characterization of such phenomena, a description of the comparative analysis, developed using them, between two formal definitions of limit of succession and function, and a synthesis of the study carried out on an intentional sample of mathematics textbooks. [ABSTRACT FROM AUTHOR]