Friday, November 4, 2022 (11/04/22)
Location: ZOOM (https://ucf.zoom.us/j/96871069010)
When: 12 pm – 1 pm
Speaker: Zeinab Mansour, Cairo University, Egypt
Abstract: : Lidstone expansions express an entire function f(z) in terms of the values of the
derivatives of even orders at 0,1. The polynomials in the expansion are called Lidstone
polynomials. They are Bernoulli polynomials; many authors introduced necessary and (or)
sufficient conditions for the absolute convergence of the series in the expansion. The classical
exponential function plays an essential role in deriving the Lidstone series. In the q theory, we
have three q-difference operators, the Jackson q-difference operator, the symmetric qdifference operator, and the Askey-Wilson q-difference operator. Each operator is associated
with a q-analog of the exponential function. This talk introduces q-extensions to the Lidstone
expansion associated with these operators. New three q-analogs of Bernoulli polynomials with
nice properties are coming out. Finally, we introduce an extension of the Leeming and
Sharma Lidstone expansion theorem.