Let s and z be complex variables, Γ(s) be the Gamma function, and for any complex v be the generalized Pochhammer symbol. Wright Type Hypergeometric Function is defined (Virchenko et al. [1]), as: where which is a di...Let s and z be complex variables, Γ(s) be the Gamma function, and for any complex v be the generalized Pochhammer symbol. Wright Type Hypergeometric Function is defined (Virchenko et al. [1]), as: where which is a direct generalization of classical Gauss Hypergeometric Function 2F1(a,b;c;z). The principal aim of this paper is to study the various properties of this Wright type hypergeometric function 2R1(a,b;c;τ;z);which includes differentiation and integration, representation in terms of pFq and in terms of Mellin-Barnes type integral. Euler (Beta) transforms, Laplace transform, Mellin transform, Whittaker transform have also been obtained;along with its relationship with Fox H-function and Wright hypergeometric function.展开更多
"What fire does not destroy,it hardens," illustrious Irish poet and playwright Oscar Wilde wrote in his only novel,The Picture of Dorian Gray,in 1890.It was the quote that somehow sprang to this author’s mi..."What fire does not destroy,it hardens," illustrious Irish poet and playwright Oscar Wilde wrote in his only novel,The Picture of Dorian Gray,in 1890.It was the quote that somehow sprang to this author’s mind as she gazed into the languid flames struggling to stay alive inside a towering hotpot sculpture at an annual winter festival in Longqingxia Scenic Area。展开更多
基金国家自然科学基金(the National Natural Science Foundation of China under Grant No.60473061)国家高技术研究发展计划(863)(theNational High- Tech Research and Development Plan of China under Grant No.2005AA113120)
文摘Let s and z be complex variables, Γ(s) be the Gamma function, and for any complex v be the generalized Pochhammer symbol. Wright Type Hypergeometric Function is defined (Virchenko et al. [1]), as: where which is a direct generalization of classical Gauss Hypergeometric Function 2F1(a,b;c;z). The principal aim of this paper is to study the various properties of this Wright type hypergeometric function 2R1(a,b;c;τ;z);which includes differentiation and integration, representation in terms of pFq and in terms of Mellin-Barnes type integral. Euler (Beta) transforms, Laplace transform, Mellin transform, Whittaker transform have also been obtained;along with its relationship with Fox H-function and Wright hypergeometric function.
文摘"What fire does not destroy,it hardens," illustrious Irish poet and playwright Oscar Wilde wrote in his only novel,The Picture of Dorian Gray,in 1890.It was the quote that somehow sprang to this author’s mind as she gazed into the languid flames struggling to stay alive inside a towering hotpot sculpture at an annual winter festival in Longqingxia Scenic Area。
