3 research outputs found
Evaluation of a Special Hankel Determinant of Binomial Coefficients
This paper makes use of the recently introduced technique of -operators to evaluate the Hankel determinant with binomial coefficient entries . We actually evaluate the determinant of a class of polynomials having this binomial coefficient as constant term. The evaluation in the polynomial case is as an almost product, i.e. as a sum of a small number of products. The -operator technique to find the explicit form of the almost product relies on differential-convolution equations and establishes a second order differential equation for the determinant. In addition to , product form evaluations for are also presented. At , we obtain another almost product evaluation for the Hankel determinant with
Evaluation of a Special Hankel Determinant of Binomial Coefficients
International audienceThis paper makes use of the recently introduced technique of -operators to evaluate the Hankel determinant with binomial coefficient entries . We actually evaluate the determinant of a class of polynomials having this binomial coefficient as constant term. The evaluation in the polynomial case is as an almost product, i.e. as a sum of a small number of products. The -operator technique to find the explicit form of the almost product relies on differential-convolution equations and establishes a second order differential equation for the determinant. In addition to , product form evaluations for are also presented. At , we obtain another almost product evaluation for the Hankel determinant with