In this paper we provide an extensive classification of one and two dimensional diffusion processes which admit an exact solution to the Kolmogorov (and hence Black-Scholes) equation (in terms of hypergeometric functions). By identifying the one-dimensional solvable processes with the class of integrable superpotentials introduced recently in supersymmetric quantum mechanics, we obtain new anal...

Due to rigorous work on integral operators and the hypergeomet-ric functions, we define here an integral operator involving generalized hypergeometric function. By means of this generalized function, we introduce new classes of analytic functions and study their properties. 1 Introduction and preliminaries. Let H be the class of functions analytic in U := {z ∈ C : |z| < 1} and A be the subclass...

We consider the q-derivatives of Srivastava and Daoust basic multivariable hypergeometric function with respect to parameters. This embodies a entire number various q-hypergeometric series one several variables. Explicit equations are given for general case summation indexes positive real coefficients. As an example derivatives q-analog non-confluent Horn type $${{H}_{3}}$$ is presented.

These Landen identities, which are in fact equivalent to each other, have been the starting points of the investigations of Qiu and Vuorinen [13], and recently of Simić and Vuorinen [14]. In this paper, motivated by [14], we make a contribution to the subject by showing that [14, Theorem 2.1], proved for the zero-balanced hypergeometric function F (a, b; a + b; ·), can be extended to the hyperg...

It is well-known that the continuous Painlevé equations PJ (J=II,. . .,VI) admit particular solutions expressible in terms of various hypergeometric functions. The coalescence cascade of hypergeometric functions, from the Gauss hypergeometric function to the Airy function, corresponds to that of Painlevé equations, from PVI to PII [1]. The similar situation is expected for the discrete Painlevé...

A certain special function of the generalized hypergeometric variety is shown to fulfill a host of useful noncommutative identities.

The table of Gradshteyn and Ryzhik contains many integrals that involve the hypergeometric function pFq . Some examples are discussed.

We study several properties of matrix variate beta type 3 distribution. We also derive probability density functions of the product of two independent random matrices when one of them is beta type 3. These densities are expressed in terms of Appell’s first hypergeometric function F1 and Humbert’s confluent hypergeometric functionΦ1 of matrix arguments. Further, a bimatrix variate generalization...

The left hand side (or A–side) of this identity was a generating series for the numbers n(d) of rational curves of various degrees d lying on a smooth quintic hypersurface in P. The right hand side (B–side) was a certain hypergeometric function. The Mirror Identity states that the two functions become identical after an explicit change of variables which is defined as a quotient of two hypergeo...