BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Zeinab Mansour (Cairo University\, Egypt) DTSTART:20211026T130000Z DTEND:20211026T140000Z DTSTAMP:20260422T201811Z UID:CAvid/53 DESCRIPTION:Title: L idstone expansions of entire functions\nby Zeinab Mansour (Cairo Unive rsity\, Egypt) as part of CAvid: Complex Analysis video seminar\n\nLecture held in N/A.\n\nAbstract\nLidstone 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 ar e Bernoulli polynomials\; many authors introduced necessary and (or) suffi cient conditions for the absolute convergence of the series in the expansi on. The classical exponential function plays an essential role in derivin g the Lidstone series. In the $q$ theory\, we have three $q$-difference op erators\, the Jackson $q$-difference operator\, the symmetric $q$-differen ce operator\, and the Askey-Wilson $q$-difference operator. Each operator is associated with a $q$-analog of the exponential function. In this talk\ , we introduce $q$-extensions to the Lidstone expansion associated with th ese operators. New three $q$-analogs of Bernoulli polynomials with nice pr operties are coming out. \n\nJoint work with Professor Mourad Ismail\, Uni versity of Central Florida\, USA.\n LOCATION:https://researchseminars.org/talk/CAvid/53/ END:VEVENT END:VCALENDAR