Journal article
On incomplete symmetric orthogonal polynomials of Jacobi type
Publication Details
Authors: | Masjed-Jamei, M.; Koepf, W. |
Publication year: | 2010 |
Journal: | Integral Transforms and Special Functions |
Pages range : | 655-662 |
Volume number: | 21 |
Start page: | 655 |
End page: | 662 |
ISSN: | 1065-2469 |
Abstract
In this paper, by using the extended Sturm-Liouville theorem for symmetric functions, we introduce the following differential equation [image omitted] in which =-2s(2s+2a-2m+1), =2s(2s+2a-2m+1)-2(2r+1)(r+a-m+1) and n=(mn+2s+(r-s+(m-1)/2)(1-(-1)n))(mn+2s+2a+1+2mb+(r-s+(m-1)/2)(1-(-1)n)) and show that one of its basic solutions is a class of incomplete symmetric polynomials orthogonal with respect to the weight function |x|2a(1-x2m)b on [-1,1]. We also obtain the norm square value of this orthogonal class.
In this paper, by using the extended Sturm-Liouville theorem for symmetric functions, we introduce the following differential equation [image omitted] in which =-2s(2s+2a-2m+1), =2s(2s+2a-2m+1)-2(2r+1)(r+a-m+1) and n=(mn+2s+(r-s+(m-1)/2)(1-(-1)n))(mn+2s+2a+1+2mb+(r-s+(m-1)/2)(1-(-1)n)) and show that one of its basic solutions is a class of incomplete symmetric polynomials orthogonal with respect to the weight function |x|2a(1-x2m)b on [-1,1]. We also obtain the norm square value of this orthogonal class.
