Thesis (M.Sc.) - Carleton University, 2003. / Includes bibliographical references (p. 59-60). Also available in electronic format on the Internet.

Thesis (M. Sc.)--University of Canterbury, 2006. / Typescript (photocopy). Includes bibliographical references (p. 57-59). Also available via the World Wide Web.

Thesis(M.S.)--Auburn University, 2006. / Abstract. Vita. Includes bibliographic references (p.25).

The present paper deals with the calculus of Tk,x,y,z - operator. The operator is a three variable analogue of the operator given earlier by W. A. Al-Salam [1] and H. B. Mittal [10]. The operator is useful for finding operational representations and generating functions of polynomials of three variables and will be dealt in a separate communication.

No description available.

No description available.

Counting lattice paths where the number of occurrences of a given pattern is monitored requires a careful analysis of the pattern. Not the length, but the characteristics of the pattern are responsible for the difficulties in finding explicit solutions. Certain features, like overlap and difference in number of ! and " steps determine the recursion formula. In the case of ballot paths, that is paths the stay weakly above the line y = x, the solutions to the recursions are typically polynomial sequences. The objects of Finite Operator Calculus are polynomial sequences, thus the theory can be used to solve the recursions. The theory of Finite Operator Calculus is strengthened and extended to the multivariate setting in order to obtain solutions, and to prepare for future applications. / by Shaun Sullivan. / Thesis (Ph.D.)--Florida Atlantic University, 2011. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2011. Mode of access: World Wide Web.

Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Mathematics. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Vita. / Bibliography : leaves 104-110. / Ph.D.

The thesis offers an investigation into the analysis of so-called iterated generating functions and the schemes that produce them. Beginning with the study of some ad hoc scheme formulations, the notion of an iterated generating function is introduced and a mechanism to produce arbitrary finite sequences established. The development of schemes to accommodate infinite sequences leads – in the case of the Catalan sequence – to the discovery of what are termed Catalan polynomials whose properties are examined. Results are formulated for these polynomials through the algebraic adaptation of classical root-finding algorithms, serving as a basis for the synthesis of new generalised results for other infinite sequences and their associated polynomials.

本篇論文主要探討長度為n的k元數列，其中若有i個偶數，j個奇數， 個不限制其奇偶，符合條件的數列個數。第一章 先預備後面計算所需要的基本知識，第二章 由生成函數開始推導公式，第三章 再討論 時的特殊情況，並利用組合方法來加以證明。第四章 針對生成函數推導出的公式再深入探討。第五章 檢討與展望。