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系統識別號 U0002-2206201220451900
中文論文名稱 兩個同類多項式乘積的積分表示式
英文論文名稱 Some Integral Representations for the Products of Two Polynomials of the Certain Classes of Polynomials
校院名稱 淡江大學
系所名稱(中) 數學學系博士班
系所名稱(英) Department of Mathematics
學年度 100
學期 2
出版年 101
研究生中文姓名 呂漢軍
研究生英文姓名 Han-Chun Lu
學號 894150050
學位類別 博士
語文別 英文
口試日期 2012-06-01
論文頁數 53頁
口試委員 指導教授-錢傳仁
委員-張茂盛
委員-陳建隆
委員-林賜德
委員-王富祥
中文關鍵字 超幾何函數與超幾何多項式  Srivastava多項式  Bedient多項式和廣義Bedient多項式  Cesaro多項式和廣義Cesaro多項式  Shively’s pseudo-Laguerre多項式  拉格朗日多項式  雅可比多項式  拉蓋爾多項式  貝索多項式和廣義貝索多項式  赫爾米特多項式  多重積分表示式  Gamma函數  Eulerian beta積分公式  線性化關係  Pochhammer符號 
英文關鍵字 Hypergeometric functions and hypergeometric polynomials  Srivastava polynomials  Bedient polynomials and the generalized Bedient polynomials of the first and second kinds  Cesaro polynomials and the generalized Cesaro polynomials  Lagrange polynomials  Shively’s pseudo-Laguerre polynomials  Bessel polynomials and the generalized Bessel polynomials  Jacobi polynomials  Laguerre polynomials  Hermite polynomials  Multiple integral representations  Gamma function  Eulerian beta integral  Linearization relationship  Pochhammer symbol 
學科別分類
中文摘要 在近一個世紀以來有多位學者相繼提出一些關於兩個同類特殊多項式乘積的積分表示式。其中不乏一些著名的特殊多項式, 如Hermit 、Laguerre 、Jacobi 、Generalized Bessel 、Generalized Rice 等特殊多項式。我們觀察到這些特殊多項式它們有 一個共同的特色,它們皆可改寫成超幾何多項式的形式。並且其關於同類多項式之間的乘積皆可整理合併成一個由其同類型多項式為核心所表達成的積分表示式。在本論文中我們將有系統的來探討此類議題, 在文中主要藉助Srivastava polynomials 為研究工具, 由其所定義出的幾類廣義超幾何多項式, 它的結構不但可涵蓋前述所提及的特殊多項式, 並可將一些具有類似結構的特殊多項式也一起收納進來。藉由文中主要結果可得到幾類廣義超幾何多項式乘積的積分表示式。利用這些結果我們可以有系統的來探討關於兩個同類多項式乘積的積分表示式。藉由某些參數的定, 我們可得到前述所提及一些特殊多項式乘積的積分表示式。另外我們也給出了一些特殊多項式乘積的積分表示式。
英文摘要 We study the product of two different members of the associated family of the certain classes of polynomials. Our principal objective in this investigation is to investigate several general families of hypergeometric polynomials and their associated multiple integral representations. By suitably specializing our main results, the corresponding integral representations are deduced for familiar classes of hypergeometric polynomials.
Also,each of the integral representations may be viewed also as a linearization relationship for the product of two different members of the associated family of hypergeometric polynomials.
論文目次 中文摘要......i
Abstract......ii
謝誌......iii
Chapter 1 Introduction......1
Chapter 2 Integral Representations for the Generalized Bedient Polynomials and
the Generalized Cesaro Polynomials......5
2.1 Introduction and Definitions......5
2.2 Multiple Integral Representations......6
2.3 Applications to Hypergeometric Polynomials......11
2.4 Integral Representations for the Generalized Bedient and the Generalized Cesaro Polynomials......15
Chapter 3 Integral Representations for the Lagrange Polynomials, Shively’s Pseudo-Laguerre Polynomials and the Generalized Bessel Polynomials......24
3.1 Introduction and Definitions......24
3.2 General Multiple Integral Representations......25
3.3 Applications to Hypergeometric Polynomials......28
3.4 Integral Representations for the Generalized Cesaro Polynomials and the Lagrange Polynomials......30
3.5 Integral Representations for Shively’s Pseudo-Laguerre Polynomials......33
3.6 Integral Representations for the Generalized Bessel Polynomials......34
Chapter 4 Integral Representations for the Generalized Bedient Polynomials of the
First and Second Kinds......38
4.1 Introduction and Definitions......38
4.2 Multiple Integral Representations......39
4.3 Applications to Hypergeometric Polynomials......42
4.4 Integral Representations for the Generalized Bedient Polynomials
of the First and Second kinds......43
References......50
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