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- W2892017533 abstract "In this paper, we introduce a generalization of the [Formula: see text]-Taylor expansion theorems. We expand a function in a neighborhood of two points instead of one in three different theorems. The first is a [Formula: see text]-analog of the Lidstone theorem where the two points are 0 and 1 and we expand the function in [Formula: see text]-analogs of Lidstone polynomials which are in fact [Formula: see text]-Bernoulli polynomials as in the classical case. The definitions of these [Formula: see text]-Bernoulli polynomials and numbers are introduced. We also introduce [Formula: see text]-analogs of Euler polynomials and numbers. On the other two expansion theorems, we expand an analytic function around arbitrary points [Formula: see text] and [Formula: see text] either in terms of the polynomials [Formula: see text] or in terms of the polynomials [Formula: see text]. As an application, we introduce a new series expansion for the basic hypergeometric series [Formula: see text]." @default.
- W2892017533 created "2018-09-27" @default.
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- W2892017533 creator A5061542078 @default.
- W2892017533 date "2019-09-23" @default.
- W2892017533 modified "2023-09-27" @default.
- W2892017533 title "q-Analogs of Lidstone expansion theorem, two-point Taylor expansion theorem, and Bernoulli polynomials" @default.
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- W2892017533 doi "https://doi.org/10.1142/s0219530518500264" @default.
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