On q-extension of Laurent expansion with applications | Zendy

Ahmed Salem | Zendy

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On q-extension of Laurent expansion with applications

Author(s) -

Ahmed Salem

Publication year - 2013

Publication title -

arab journal of mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.353

H-Index - 11

eISSN - 2588-9214

pISSN - 1319-5166

DOI - 10.1016/j.ajmsc.2013.06.001

Subject(s) - laurent series , mathematics , cauchy's integral formula , laurent polynomial , residue theorem , extension (predicate logic) , cauchy distribution , pure mathematics , bounded function , analytic continuation , analytic function , taylor series , algebra over a field , calculus (dental) , mathematical analysis , cauchy problem , initial value problem , computer science , programming language , medicine , dentistry

In this article, Cauchy’s integral formula for nth q-derivative of analytic functions is established and used to introduce a new proof to q-Taylor series by means of using the residue calculus in the complex analysis. Some theorems related to this formula are presented. A q-extension of a Laurent expansion is derived and proved by means of using Cauchy’s integral formula for a function, which is analytic on a ring-shaped region bounded by two concentric circles. Three illustrative examples are presented to be as applications for a q-Laurent expansion

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