The Calculation Andapplication Of Generalized Cauchy's Double Alterant

The calculation of the determinant has been an important subject of algebra research.The famous Cauchy's double alterant plays an important application in multiple elliptical hypergeometric series and symmetric function.In order to research Cauchy's double alterant furtherly,this article mainly summarizes the determinant calculation method and we apply the Laplace expansion formula and the partial fraction to abtain generalized Cauchy's double alterant.On this basis,we get several interesting determinant formula.The main content is summarized as follows:The first chapter is the introduction part,this paper introduces the research background of determinant,the determinant calculation in domestic and foreign development present situation,the knowledge and methods of this paper.The second chapter introduces the definition of determinant,the nature of the determinant and some the calculation method of determinant,especially the research of Laplace expansion formula is studied for subsequent chapters to evalue the generalized Cauchy determinant.The third chapter introduces the definition of difference quotient and simply shows some common properties of difference quotient,also we give several important divided differences for the following research.The fourth chapter applys Laplace expansion formula,Divided differences and partial fraction method to prove a generalized Cauchy determinant calculation formula and through specializing the parameters,the author gives some beautiful determinant equation.