Volume 25: Pages 38-42, 2012
Basic completely monotone functions as coefficients and solutions of linear q-difference equations with some applications
Hossam A. Ghany a)
Mathematics Department, Faculty of Science, Taif University, Hawea (P.O. 888) Taif, Saudi Arabia,
Mathematics Department, Faculty of Industrial Education, Helwan University, Sawah Street, Ameria (P.O. 11282), Cairo, Egypt
This paper is devoted to give some properties of the derivatives of basic hypergeometric series with respect to parameters. The derivatives of the basic hypergeometric functions with respect to parameters are employed to show and explain some properties of the solutions of -difference equations with basic completely monotone functions as coefficients. As an application, some physical problems related to Jacobi Θ functions and its derivatives are illustrated.
Cet article est consacré à donner certaines propriétés des dérivées des séries hypergéométriques de base par rapport aux paramètres. Ces dérivées sont utilisées pour montrer et expliquer certaines propriétés des solutions des équations aux différences ayant fonctions de base totalement monochrome comme coefficients. Comme application, certains problèmes physiques liés aux fonctions Θde Jacobi et ses dérivées sont illustrés.
Key words: Basic Hypergeometric Functions, Derivative, Difference, Jacobi Θ Functions
Received: September 6, 2011; Accepted: November 15, 2011; Published Online: March 19, 2012
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