報告題目: Eulerian Numbers, Eulerian Polynomials, and B-Splines and Their Generalizations and Applications in Numerical Analysis
報 告 人：何天曉教授 美國伊利諾伊衛斯理大學
報告時間: 2019年6月17日上午9：00-10：00
報告地點：數學樓一樓第二報告廳
報告摘要:
We present the interrelationships between Eulerian polynomials and Euler-Frobenius polynomials, Eulerian numbers and discrete B-splines, Eulerian fractions and Euler-Frobenius fractions. Those discovered connections are used to develop their properties efficiently. The applications in spline image interpolation, wavelet analysis, and the evaluation of Riemann zeta function values at odd integers are discussed. We also extend the B-splines, Eulerian numbers,Eulerian polynomials, and Eulerian fractions to the complex orders and present their applications to the polylogarithm functions. Some recent works on the q-analogues of B-splines, Eulerian numbers, and Eulerian- Frobenius polynomials by Disibuyuk and Ulutas and generalized Eulerian numbers of different kinds by Rzadkowski and Urlinska are introduced. Some open problems are presented.
報告人簡介：
何天曉教授，伊利諾伊衛斯理大學數學教授，自然科學和數學的貝甯（Beling）（冠名）教授。1987年獲得大連理工大學理學博士學位，1991年獲得Texas A&M大學哲學博士學位。自1991年任教于伊利諾伊衛斯理大學至今。發表了140餘篇專業文章和6本書，其中的108篇（本）登錄在數學評論上。
