Some New Symmetric Identities for the q-Zeta Type Functions

The main object of this paper is to obtain several symmetric properties of the q-Zeta type functions. As applications of these properties, we give some new interesting identities for the modified q-Genocchi polynomials. Finally, our applications are shown to lead to a number of interesting results which we state in the present paper.Comment: 8 pages; submitte

Extensions of the Classical Transformations of 3F2

It is shown that the classical quadratic and cubic transformation identities satisfied by the hypergeometric function ${}_3F_2$ can be extended to include additional parameter pairs, which differ by integers. In the extended identities, which involve hypergeometric functions of arbitrarily high order, the added parameters are nonlinearly constrained: in the quadratic case, they are the negated roots of certain orthogonal polynomials of a discrete argument (dual Hahn and Racah ones). Specializations and applications of the extended identities are given, including an extension of Whipple's identity relating very well poised ${}_7F_6(1)$ series and balanced ${}_4F_3(1)$ series, and extensions of other summation identities.Comment: 22 pages, expanded version, to appear in Advances in Applied Mathematic