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...

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....

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...