In many problems arising in physical sciences and statistics, hypergeometric functions, in logarithmic cases, are applicable, which is known from the monograph of Mathai and Haubold [4] and Mathai [3], etc. A detailed account of such applications is available from the two monographs by Mathai and Saxena [5], [6]. Expansions of the Gauss’s hypergeometric functions in logarithmic cases are given ...

Abstract. We find two-sided inequalities for the generalized hypergeometric function with positive parameters restricted by certain additional conditions. Our lower bounds are asymptotically precise at x = 0, while the upper bounds are either asymptotically precise or at least agree with q+1Fq((aq+1), (bq);−x) at x = ∞. Inequalities are derived as corollaries of a theorem asserting the monotony...

Carlson and Shaffer [B.C. Carlson, D.B. Shaffer, Starlike and prestarlike hypergeometric functions, SIAM J. Math. Anal. 15 (1984) 737–745] have introduced a linear operator associated with the Gaussian hypergeometric function which has been generalized by Dziok and Srivastava [J. Dziok, H.M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl....

In recent years, several interesting families of generating functions for various classes of hypergeometric and generalized hypergeometric functions in one, two and more variables were investigated systematically. Here, in this sequel, we aim at establishing several (presumably) new generating relations for the generalized Gauss type hypergeometric functions which are introduced by means of som...

Integral Mittag-Leffler, Whittaker and Wright functions with integrands similar to those which already exist in mathematical literature are introduced for the first time. For particular values of parameters, they can be presented a closed form. In most reported cases, these new integral expressed as generalized hypergeometric functions, but also terms elementary special functions. Behaviour som...

The generalized hypergeometric function has three singular points 0, 1, and ∞. Connection problem between fundamental solutions at 0 ∞ was completely solved. However, connection 1 been not solved because of holomorphic 1. In this paper, we solve for the function, using analytic continuation integral representation. Namely, all coefficients are products sine cosecant. other words, give a good sy...

The paper is devoted to the study of the fractional calculus of the generalized Wright function pΨq(z) defined for z ∈ C, complex ai, bj ∈ C and real αi, βj ∈ R (i = 1, 2, · · · p; j = 1, 2, · · · , q) by the series

An attempt is made here to study the Mittag–Leffler function with two variables. Its various properties including integral and operational relationships other known functions of one variable, pure differential recurrence relations, Euler transform, Laplace Mellin Whittaker Mellin–Barnes representation, its relationship Wright hypergeometric are investigated established. Also, variables associat...

In this paper, using similar symbolical method of Burchnall and Chaundy formulas of expansion for the generalized hypergeometric function were constructed. By means of the found formulas of expansion the formulas of an analytic continuation for hypergeometric function of Clausen is defined. The obtained formulas of an analytic continuation express known hypergeometric Appell function F2 (a; b1,...