In the preprint [1] one of the authors formulated some conjectures on monotonicity of ratios for exponential series sections. They lead to more general conjecture on monotonicity of ratios of Kummer hypergeometric functions and was not proved from 1993. In this paper we prove some conjectures from [1] for Kummer hypergeometric functions and its further generalizations for Gauss and generalized ...

In this paper, we generalize the well known differential operator by using a generalized hypergeometric function. By applying this operator, we introduce a new class of non-Bazilević functions and derive subordination and superordination results for the class in the unit disk. Relevant connections of the results presented in this paper are also pointed out with various other known results.

We give a closed-form evaluation of a number of Erd elyi-Kober fractional integrals involving elliptic integrals of the rst and second kind, in terms of the 3F2 generalized hypergeometric function. Reduction formulae for 3F2 enable us to simplify the solutions for a number of particular cases. c © 1999 Elsevier Science B.V. All rights reserved.

The expansion of arbitrary power series in various classes of polynomial sets is considered. Some applications are also given. Notations. We will use the following contracted notation for the generalized hypergeometric function •i> •flB P q\bl,...,bQ pFAb, ^ M* z_k where p. « r(o4 k) («iOfc-n fy)*. (*v*s rw* and (°)* / = ! / = ! r(o)

The object of this paper is to solve a fractional integro-differential equation involving a generalized Lauricella confluent hypergeometric function in several complex variables and the free term contains a continuous function f (τ). The method is based on certain properties of fractional calculus and the classical Laplace transform. A Cauchy-type problem involving the Caputo fractional derivat...

In this paper, we prove a conjecture of Alexandrov that the generalized Brézin-Gross-Witten tau-functions are hypergeometric tau functions BKP hierarchy after re-scaling. particular, shows original BGW tau-function, which has enumerative geometric interpretations, can be represented as linear combination Schur Q-polynomials with simple coefficients.

This paper deals with generalized hypergeometric differential equations of order n ≥ 3 having maximal unipotent monodromy at 0. We show that, among these equations, those leading to mirror maps with integral Taylor coefficients at 0 (up to simple rescaling) have special parameters, namely R-partitioned parameters. This result yields the classification of all generalized hypergeometric different...

The authors would like to thank the referees for their helpful suggestions which essentially improved the presentation of this paper. Abstract. In this paper, we introduce a new subclass of meromorphic functions and investigate inclusion relationships and properties of a certain class of meromorphically p-valent functions, which are defined by means of the familiar operator involving the genera...