q-Analogs of Lidstone expansion theorem, two-point Taylor expansion theorem, and Bernoulli polynomials

DOI10.1142/S0219530518500264zbMath1423.05029OpenAlexW2892017533MaRDI QIDQ5236749

Zeinab S. I. Mansour, Mourad E. H. Ismail

Publication date: 10 October 2019

Published in: Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219530518500264

zbMATH Keywords

Cauchy kernelbasic hypergeometric series\(q\)-analog of Bernoulli polynomials\(q\)-analog of Lidstone expansion theoremtwo-point \(q\)-Taylor series

Mathematics Subject Classification ID

(q)-calculus and related topics (05A30) Bernoulli and Euler numbers and polynomials (11B68) Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Power series (including lacunary series) in one complex variable (30B10) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Difference equations, scaling ((q)-differences) (39A13)

Related Items (4)

Generalized \(q\)-Bernoulli polynomials generated by Jackson \(q\)-Bessel functions ⋮ On q-analogs of zeta functions associated with a pair of q-analogs of Bernoulli numbers and polynomials ⋮ The \(q\)-Lidstone series involving \(q\)-Bernoulli and \(q\)-Euler polynomials generated by the third Jackson \(q\)-Bessel function ⋮ \(q\)-type Lidstone expansions and an interpolation problem for entire functions

Cites Work

• New series expansions of the Gauss hypergeometric function
• \(q\)-fractional calculus and equations
• The \(q\)-tangent and \(q\)-secant numbers via continued fractions
• \(q\)-Taylor and interpolation series for Jackson \(q\)-difference operators
• Combinatorics of generalized \(q\)-Euler numbers
• About the growth of entire functions solutions of linear algebraic \(q\)- difference equations
• \(q\)-Taylor theorems, polynomial expansions, and interpolation of entire functions.
• Applications of \(q\)-Taylor theorems
• Q-shock soliton evolution
• \(q\)-Bernoulli numbers and polynomials
• q‐Bernoulli numbers and polynomials
• Two‐Point Taylor Expansions of Analytic Functions
• q-Hermite Polynomials, Biorthogonal Rational Functions, and q-Beta Integrals
• Upper Bounds on Arc Length
• The $q$-tangent and $q$-secant numbers via basic Eulerian polynomials
• Explicit Formulas for Bernoulli Numbers
• q-Bernoulli and Eulerian Numbers
• Some polynomials related to theta functions
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: q-Analogs of Lidstone expansion theorem, two-point Taylor expansion theorem, and Bernoulli polynomials