Some product formulas for theta functions in one and two variables

q-GENERATING FUNCTIONS FOR ONE AND TWO VARIABLES

Abstract. We use a multidimensional extension of Bailey’s transform to derive two very general q-generating functions, which are q-analogues of a paper by Exton [7]. These expressions are then specialised to give more practical formulae, which are q-analogues of generating relations for Karlssons generalised Kampe de Fériet function. A number of examples are given including q-Laguerre polynomia...

Some integral inequalities for functions of two variables

In this article, we establish some integral inequalities for function with two independent variables. Also we show applications of these inequalities for finding bounds of solutions to partial differential equations.

Some Asymptotic Formulas for Multiplicative Functions

Somos Sequence Near-Addition Formulas and Modular Theta Functions

We have discovered conjectural near-addition formulas for Somos sequences. We have preliminary evidence suggesting the existence of modular theta functions.

Non–linear fractal interpolating functions of one and two variables

In this paper we consider two non–linear generalizations of such fractal interpolating functions. The first concerns how to extend the linear interpolation of Eq. (4) to higher–degree interpolations. The second generalization arises when one considers the construction of fractal interpolating functions for functions of two (or more) variables – here, even a linear interpolation of the form of E...