New forms of the Cauchy operator and some of their applications |
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| Authors: | H M Srivastava M A Abdlhusein |
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| Institution: | 1.Department of Mathematics and Statistics,University of Victoria,Victoria, British Columbia,Canada;2.China Medical University,Taichung Taiwan,Republic of China;3.Department of Mathematics, College of Education for Pure Sciences,Thi-Qar University,Thi-Qar,Iraq |
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| Abstract: | In this paper, we first construct the Cauchy q-shift operator T(a, b;D xy ) and the Cauchy q-difference operator L(a, b; θ xy ). We then apply these operators in order to represent and investigate some new families of q-polynomials which are defined in this paper. We derive some q-identities such as generating functions, symmetry properties and Rogers-type formulas for these q-polynomials. We also give an application for the q-exponential operator R(bD q ). |
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