New Applications of Gaussian Hypergeometric Function for Developments on Third-Order Differential Subordinations

Certain Second Order Linear Differential Subordinations

In this present investigation, we obtain some results for certain second order linear differential subordination. We also discuss some applications of our results.

ON TE EXISTENCE OF PERIODIC SOLUTION FOR CERTAIN NONLINEAR THIRD ORDER DIFFERENTIAL EQUATIONS

On second-order differential subordinations for a class of analytic functions defined by convolution

Making use of the convolution operator we introduce a new class of analytic functions in the open unit disk and investigate some subordination results. c ©2017 All rights reserved.

College of Arts and Sciences Third Order a - Hypergeometric Functions

To solve globally bounded order 3 linear differential equations with rational function coefficients, this thesis introduces a partial 3F2-solver (Section 3.2) and F1-solver (Chapter 4) where 3F2 is the hypergeometric function 3F2(a1, a2, a3; b1, b2 |x) and F1 is the Appell’s F1(a, b1, b2, c |x, y). To investigate the relations among order 3 multivariate hypergeometric functions, this thesis pre...

Apostol-euler Polynomials of Higher Order and Gaussian Hypergeometric Functions

The purpose of this paper is to give analogous definitions of Apostol type (see T. M. Apostol [Pacific J. Math. 1 (1951), 161-167]) for the so-called Apostol-Euler numbers and polynomials of higher order. We establish their elementary properties, obtain several explicit formulas involving the Gaussian hypergeometric function and the Stirling numbers of the second kind, and deduce their special ...