Some integral representations for the products of two polynomials of the certain classes of polynomials

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Title:	Some integral representations for the products of two polynomials of the certain classes of polynomials
Other Titles:	兩個同類多項式乘積的積分表示式
Authors:	呂漢軍;Lu, Han-Chun
Contributors:	淡江大學數學學系博士班錢傳仁
Keywords:	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;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
Date:	2012
Issue Date:	2013-04-13 11:08:59 (UTC+8)
Abstract:	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.
Appears in Collections:	[Graduate Institute & Department of Mathematics] Thesis

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