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The hypergeometric functions occur naturally in variety of problems in analysis, statistics, operational research, theoretical and mathematical physics and engineering sciences. In the physical problems where these special functions occur, sometimes it is required to have their first approximations. In the advance analysis of a given problem, we need to dispose with some simple but sufficiently accurate algorithms for the approxima-. tions of the hypergeometric functions. In this paper we present some series and integral representations of them and discuss several simply-structured single term approximation formulae: for the Hubbell type radiation integrals, generalized hypergeometric functions and Appell's functions. We propose also a new approach to estimate the pFq-functions by relating them to three simple elementary functions. The notions generalized (multiple) fractional integrals and derivatives are used. [ABSTRACT FROM AUTHOR]

Recently, Brychkov et al. established several new and interesting reduction formulas for the Humbert functions (the confluent hypergeometric functions of two variables). The primary objective of this study was to provide an alternative and simple approach for proving four reduction formulas for the Humbert function ψ 2 . We construct intriguing series comprising the product of two confluent hypergeometric functions as an application. Numerous intriguing new and previously known outcomes are also achieved as specific instances of our primary discoveries. It is well-known that the hypergeometric functions in one and two variables and their confluent forms occur naturally in a wide variety of problems in applied mathematics, statistics, operations research, physics (theoretical and mathematical) and engineering mathematics, so the results established in this paper may be potentially useful in the above fields. Symmetry arises spontaneously in the abovementioned functions. [ABSTRACT FROM AUTHOR]

In reply to a question raised in the literature, and to settle an argument debated in the last decades, we give the exact closed form expression of the density of X / Y , where X and Y are normal random variables, in terms of Hermite and confluent hypergeometric functions. All cases will be considered: standardized and nonstandardized variables, independent or correlated variables. Examples in applied disciplines are presented, and generalizations to ratios of variables from scale mixtures of bivariate normal distributions show the potential of further new applications in applied statistics and operations research. [ABSTRACT FROM AUTHOR]

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]

We introduce a novel analytical framework for the end-to-end (e2e) maximum throughput under delay constraints, namely effective capacity (EC), for multisource and multidestination amplify-and-forward cooperative networks. The network operates in the presence of Rayleigh fading and employs frequency-division duplex nodes having the ability to simultaneously transmit as sources and receive as relays. Cochannel interference and noise are present at the relay nodes, whereas the destination nodes are noise limited. A linear precoding technique is applied during reception to combine the input signals. As precoding, zero forcing (ZF), maximal-ratio combining (MRC), and minimum mean-squared error (MMSE) are studied. Each relay forwards the received signal to the destination by employing the maximum-ratio transmission (MRT) scheme. Both exact analytical expressions and tight high signal-to-noise ratio bounds of e2e EC are obtained for the ZF/MRT scheme while the optimal power allocation problem maximizing the e2e EC is also addressed. For the MRC/MRT and MMSE/MRT schemes, we derive approximate, yet highly accurate EC analytical expressions, as well as asymptotically tight closed-form expressions. Selected numerical and simulation results show that MMSE/MRT always yields the best performance followed by the ZF/MRT and MRC/MRT schemes. Moreover, it is shown that as the number of relay nodes increases, the ZF/MRT and MMSE/MRT schemes achieve almost identical and always better e2e EC performance than the MRC/MRT one. [ABSTRACT FROM AUTHOR]

In this paper we present a detailed analysis of queueing models with vacations and impatient customers, where the source of impatience is the absence of the server. Instead of the standard assumption that customers perform independent abandonments, we consider situations where customers abandon the system simultaneously. This is, for example, the case in remote systems where customers may decide to abandon the system, when a transport facility becomes available. [ABSTRACT FROM AUTHOR]

An exact expression for the consumer's utility has not been known when a multi-category basket is assumed. This technical note derives an exact and explicit expression. [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]

In this article, we consider the problem of developing a unified point of view on the theory of multi-variable and multi-index Hermite polynomials. We combine the principle of monomiality with the methods of operational nature and show that this approach provides a more flexible tool than a full Lie-algebraic treatment. We also provide several examples illustrating this unified point of view. [ABSTRACT FROM AUTHOR]

This paper extends the work of White and Christie, reported in OPERATION RESEARCH, vol 6, pp 79-95 (January-February, 1958), on preemptive priority queuing. A random walk procedure yields recursive relations between the state probabilities in the steady state. Recursive relations for the moments of the length of the lower priority queue follow. Combined with the use of moment generating functions, this approach provides moments of the waiting time for elements of the lower priority class that arrive when the system is in a given state, i e, the two queues are of given lengths. The moments of waiting time and time in the system are also obtained recursively for the steady state Routines for computing and checking are provided. [ABSTRACT FROM AUTHOR]