کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
6420690 | 1631798 | 2015 | 9 صفحه PDF | دانلود رایگان |
The purpose of the present paper is to give the parameter derivative representations of the formâPn,k(λ;x,y)âλ=âm=0n-1âj=0mdn,j,mPm,j(λ;x,y)+âj=0ken,j,kPn,j(λ;x,y)for a family of orthogonal polynomials of variables x and y, with λ being a parameter and 0⩽k⩽n;n,k=0,1,2,â¦. First, we shall present the representations of the parameter derivatives of the generalized Gegenbauer polynomials Cn(λ,μ)(x) with the help of the parameter derivatives of the classical Jacobi polynomials Pn(α,β)(x), i.e. ââαPn(α,β)(x) and ââβPn(α,β)(x). Then, by using these derivatives, we investigate the parameter derivatives for two-variable analogues of the generalized Gegenbauer polynomials. Furthermore, we discuss orthogonality properties of the parametric derivatives of these polynomials.
Journal: Applied Mathematics and Computation - Volume 256, 1 April 2015, Pages 769-777