A new set of multiple orthogonal polynomials both type I and II with respect to two weight functions involving Gauss' hypergeometric function on the interval (0,1) is studied. This has direct applications in investigation singular values products Ginibre random matrices are connected branched continued fractions total-positivity problems combinatorics. The pair orthogonality measures shown be a...

Under a certain condition, we find the explicit formulas for the trace functions of certain intertwining operators among gl(n)-modules, introduced by Etingof in connection with the solutions of the Calogero-Sutherland model. If n = 2, the master function of the trace function is exactly the classical Gauss hypergeometric function. When n > 2, the master functions of the trace functions are a ne...

Various extensions of classical gamma, beta, Gauss hypergeometric and confluent functions have been proposed recently by many researchers. In this paper, we further generalized extended beta function with some its properties such as symmetric properties, summation formulas, integral representations, connection other special error, Mittag – Leffler, incomplete hypergeometric, Wright, Fox H Meije...

The classical Gauss hypergeometric function and the Kumar confluent are defined using a Pochammer symbol , factorial function. This research paper will present two-parameter Pochhammer symbol, discuss some of its properties such as recursive formulae integral representation. In addition, generalized functions new were also discussed.

We find sufficient conditions for log-convexity and log-concavity for the functions of the forms a 7→ ∑ fk(a)kx , a 7→ ∑ fkΓ(a + k)x k and a 7→ ∑ fkx k/(a)k. The most useful examples of such functions are generalized hypergeometric functions. In particular, we generalize the Turán inequality for the confluent hypergeometric function recently proved by Barnard, Gordy and Richards and log-convexi...

We investigate the approximate l-state solutions of Schrödinger equation for Hulthén plus a class Yukawa potential. In this context, we construct bound-state energy and wavefunction expressed by Gauss hypergeometric function means asymptotic iteration approach in detail.

It is proved that the Laurent expansion of the following Gauss hypergeometric functions, are an arbitrary integer nonnegative numbers, a, b, c are an arbitrary numbers and ε is an arbitrary small parameters, are expressible in terms of the harmonic polylogarithms of Remiddi and Vermaseren with polynomial coefficients. An efficient algorithm for the calculation of the higher-order coefficients o...