The present paper deals with the effects of Ohmic dissipative Casson fluid flow over a stretching sheet in the presence of aligned magnetic field. The present phenomenon also includes the interaction of thermal radiation and velocity slip. The governing boundary layer equations are transformed into a set of ordinary differential equations using the similarity transformations. The dimensionless ...

We establish two binomial coefficient–generalized harmonic sum identities using the partial fraction decomposition method. These identities are a key ingredient in the proofs of numerous supercongruences. In particular, in other works of the author, they are used to establish modulo p (k > 1) congruences between truncated generalized hypergeometric series, and a function which extends Greene’s ...

We describe the structure of all codimension-two lattice configurations A which admit a stable rational A-hypergeometric function, that is a rational function F all whose partial derivatives are non zero, and which is a solution of the A-hypergeometric system of partial differential equations defined by Gel’fand, Kapranov and Zelevinsky. We show, moreover, that all stable rational A-hypergeomet...

Based on the generalized extended beta function, we shall introduce and study a new hypergeometric-type zeta function together with related integral representations, differential relations, finite sums, series expansions. Also, present relationship between Laguerre polynomials. Our hypergeometric type involves several known functions including Riemann, Hurwitz, Hurwitz-Lerch, Barnes as particul...

We give an introduction to the Gauss hypergeometric function, the hypergeometric equation and their properties in an elementary way. Moreover we explicitly and uniformly describe the connection coefficients, the reducibility of the equation and the monodromy group of the solutions.

The incomplete gamma function and incomplete beta function are important special functions in statistics. In modern theory of special functions, we regard hypergeometric functions as pairings of twisted cycles and twisted cocycles [1, Chap 2]. However, domains of integrations of these incomplete functions are not cycles. Solutions of A-hypergeometric systems ([3], [7, p.221]) have integral repr...

In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.

Given the hypergeometric function F (a, b; c; z) = ∞ P n=0 (a)n(b)n (c)n(1)n zn, we place conditions on a, b and c to guarante that zpF (a, b; c; z) will be in various subclasses of p-valent starlike and p-valent convex functions. Operators related to the hypergeometric function are also examined.

We present the τ -functions for the hypergeometric solutions to the q-Painlevé system of type E (1) 7 in a determinant formula whose entries are given by the basic hypergeometric function 8W7. By using the W (D5) symmetry of the function 8W7, we construct a set of twelve solutions and describe the action of W̃ (D (1) 6 ) on the set.