Tian-Xiao He Copyright (c) 2011 All rights reserved. http://works.bepress.com/tian_xiao_he Recent documents in Tian-Xiao He en-us Mon, 12 Sep 2011 01:30:17 PDT 3600 Riordan arrays associated with Laurent series and generalized Sheffer-type groups http://works.bepress.com/tian_xiao_he/14 http://works.bepress.com/tian_xiao_he/14 Sat, 10 Sep 2011 13:54:25 PDT A relationship between a pair of Laurent series and Riordan arrays is formulated. In addition, a type of generalized Sheffer groups is defined using Riordan arrays with respect to power series with non-zero coefficients. The isomorphism between a generalized Sheffer group and the group of the Riordan arrays associated with Laurent series is established. Furthermore, Appell, associated, Bell, and hitting-time subgroups of the groups are defined and discussed. A relationship between the generalized Sheffer groups with respect to different power series is presented. The equivalence of the defined Riordan array pairs and generalized Stirling number pairs is given. A type of inverse relations of various series is constructed using pairs of Riordan arrays. Finally, several applications involving various arrays, polynomial sequences, special formulas and identities are also presented as illustrative examples.

]]> Tian-Xiao He Riordan Arrays An Euler-Type Formula for Zeta (2k+1) http://works.bepress.com/tian_xiao_he/13 http://works.bepress.com/tian_xiao_he/13 Fri, 05 Mar 2010 10:14:42 PST Tian-Xiao He Number Theory On Abel-Gontscharoff-Gould's polynomials http://works.bepress.com/tian_xiao_he/12 http://works.bepress.com/tian_xiao_he/12 Fri, 05 Mar 2010 10:10:31 PST Tian-Xiao He Interpolation and Approximation On Multivariate Abel-Gontscharoff Interpolation http://works.bepress.com/tian_xiao_he/11 http://works.bepress.com/tian_xiao_he/11 Fri, 05 Mar 2010 10:06:02 PST Tian-Xiao He Interpolation and Approximation On an Extension of Abel-Gontscharoff's Expansion Formula http://works.bepress.com/tian_xiao_he/10 http://works.bepress.com/tian_xiao_he/10 Fri, 05 Mar 2010 09:57:07 PST Tian-Xiao He Interpolation and Approximation Short Time Fourier Transform, Integral Wavelet Transform, and Wavelet Functions Associated with Splines http://works.bepress.com/tian_xiao_he/9 http://works.bepress.com/tian_xiao_he/9 Fri, 05 Mar 2010 09:47:22 PST Tian-Xiao He Wavelet Analysis Biorthogonal Wavelets with Certain Regularities http://works.bepress.com/tian_xiao_he/8 http://works.bepress.com/tian_xiao_he/8 Fri, 05 Mar 2010 09:41:41 PST Tian-Xiao He Wavelet Analysis On the Generalized Mobius Inversion Formulas http://works.bepress.com/tian_xiao_he/5 http://works.bepress.com/tian_xiao_he/5 Wed, 03 Mar 2010 08:44:15 PST Tian-Xiao He Mobius function and Mobius inversion A Symbolic Operator Approach to Several Summation Formulas for Power Series http://works.bepress.com/tian_xiao_he/4 http://works.bepress.com/tian_xiao_he/4 Wed, 03 Mar 2010 08:35:39 PST Tian-Xiao He symbolic operator Sequence Characterization of Riordan Arrays http://works.bepress.com/tian_xiao_he/3 http://works.bepress.com/tian_xiao_he/3 Tue, 02 Mar 2010 15:06:26 PST Tian-Xiao He A symbolic operator approach to several summation formulas for power series II http://works.bepress.com/tian_xiao_he/2 http://works.bepress.com/tian_xiao_he/2 Thu, 05 Feb 2009 06:28:58 PST Here expounded is a kind of symbolic operator method that can be used to construct many transformation formulas and summation formulas for various types of power series including some old ones and more new ones.

]]> Tian-Xiao He symbolic operator The Sheffer Group and the Riordan Group http://works.bepress.com/tian_xiao_he/1 http://works.bepress.com/tian_xiao_he/1 Tue, 19 Feb 2008 10:43:55 PST Tian-Xiao He