q-Taylor theorems, polynomial expansions, and interpolation of entire functions
نویسندگان
چکیده
We establish q-analogues of Taylor series expansions in special polynomial bases for functions analytic in bounded domains and for entire functions whose maximum modulus Mðr; f Þ satisfies jln Mðr; f ÞjpA ln r: This solves the problem of constructing such entire functions from their values at 1⁄2aq þ q =a =2; for 0oqo1: Our technique is constructive and gives an explicit representation of the sought entire function. Applications to q-series identities are given. r 2003 Elsevier Science (USA). All rights reserved.
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عنوان ژورنال:
- Journal of Approximation Theory
دوره 123 شماره
صفحات -
تاریخ انتشار 2003