报告题目: Eulerian Numbers,Eulerian Polynomials, and B-Splines and Their Generalizations and Applicationsin Numerical Analysis

报 告 人：何天晓 教授 美国伊利诺伊卫斯理尊龙凯时

报告时间: 2019年6月17日上午9：00-10：00

报告地点：数学楼一楼第二报告厅

报告摘要:

We present the interrelationships between Eulerian polynomialsand Euler-Frobenius polynomials, Eulerian numbers and discrete B-splines,Eulerian fractions and Euler-Frobenius fractions. Those discovered connectionsare used to develop their properties efficiently. The applications in splineimage interpolation, wavelet analysis, and the evaluation of Riemann zetafunction values at odd integers are discussed. We also extend the B-splines,Eulerian numbers,Eulerian polynomials, and Eulerian fractions to the complexorders and present their applications to the polylogarithm functions. Somerecent works on the q-analogues of B-splines, Eulerian numbers, and Eulerian- Frobeniuspolynomials by Disibuyuk and Ulutas and generalized Eulerian numbers of differentkinds by Rzadkowski and Urlinska are introduced. Some open problems arepresented.

报告人简介：

何天晓教授，伊利诺伊卫斯理尊龙凯时数学教授，自然科学和数学的贝宁（Beling）（冠名）教授。1987年获得大连理工尊龙凯时理学博士学位，1991年获得Texas A&M尊龙凯时哲学博士学位。自1991年任教于伊利诺伊卫斯理尊龙凯时至今。发表了140余篇专业文章和6本书，其中的108篇（本）登录在数学评论上。