摘要
本論文主要是針對多變數的拉格朗日多項式(Multivariable Lagrange polynomials)方面所作之研究。 第一章:緒論。 第二章:導出多變數的拉格朗日多項式相關的一些等式,並且在雙變數的情況下,可經由一些轉換即可推廣成,相關文獻中所研究(雅可比多項式、拉蓋爾多項式、超幾何多項式)的主要等式。另外也研究一些線性偏微分算子與多變數的拉格朗日多項式之間的關係。 第三章:將三個變數的拉格朗日多項式與Appell函數的雙側生成函數(Bilateral generating functions),推廣成多變數的拉格朗日多項式與Lauricella函數的雙側生成函數。 第四章:藉由變數變換再取極限,去導出新的多項式,並求出對應於拉格朗日多項式的一些等式和遞迴關係。 第五章:利用Bailey 三次轉換去導出雙重級數的等式,並藉此去求出 Srivastava-Daoust 的轉換公式與歸約公式。
並列摘要
The main purpose of this thesis is to investigate multivariable Lagrange polynomials. In Chapter 1, introduction. In Chapter 2, we derive some identities of Lagrange polynomials of two variables and observe the relations between Lagrange polynomials and Jacobi, Laguerre and Hypergeometric polynomials, respectively. On the other hand, we investigate linear partial differential operators on multivariable Lagrange polynomials. In Chapter 3, we generalize bilateral generating functions for the Lagrange polynomials with three variables and the Appell functions, as bilateral generating functions for the Lagrange polynomials with multivariable and the Lauricella functions. In Chapter 4, using the method of substitution and taking limit, we obtain some new polynomials. We obtain some identities and recurrence relations. In Chapter 5, Based upon Bailey’s cubic transformations, we construct some identities and use item to find transformation and reduction formulas for the Srivastava-Daoust hypergeometric function in two variables.