臺灣博碩士論文加值系統

我們主要是延續Kung-Yu Chen 和H.M. Srivastava兩位教授的一些研究。利用生成函數以及複變數的一些理論繼而得到一些關於超幾何多項式的�痤它﹛C特別地，我們得到更多的有關古典的Laguerre 多項式之一些恆等式。相較於Bavinck使用微分算子的技巧得到Laguerre 多項式關係式，我們引進了更簡單的方法。

The main object of this paper is to a continatire work of Kung-Yu Chen and H.M. Srivastava. We use generating functions and a few theory of complex variables to obtain some new results for Hypergeometric Polynomials.Particularly, we obtain more identities about classic Laguerre pynomial. Compare with the relationship about Laguerre pynomials made by Bavink who use of the differential operator to prove, we find a method more simple then him.

目錄

Intruduction……………………………………………………p.1

第一章 超幾何多項式Hypergeometric polynomials

1.1 定義與基本性質…………………………………………………..p.2

1.2 超幾何函數之恆等式……………………………………………..p.8

1.3 Remark……………………………………………………………..p.19

第二章 Srivastava-Singhal polynomials

2.1 定義與基本性質…………………………………………………..p.22

2.2 Srivastava-Singhal polynomials 之恆等式…………p.23

參考文獻...................................................p.34

[1] H.Bavinck , A new result for Laguerre polynomials , J.Phys. A: Math.
Gen. 29(1996) , L277-L279.
[2] Kung-Yu Chen and H.M. Srivastava , A new result for hypergeometric polynomials , Ame. Proc.(to be appeared).
[3] Kung-Yu Chen , A new summation identity for the srivastava-Singhal polynomials , J. Math. Anal. Appl. 298 (2004) , 411-417.
[4] H.M. Srivastava , Some Families of generating functions associated with the Stirling numbers of the second kind , J. Math. Anal. Appl. 251 (2000) , 752-769.