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。

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.

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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