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Session III.7 - Special Functions and Orthogonal Polynomials


Moments of Jacobi Polynomials with non-classical parameters

John Lopez

Tulane, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this poster we will present two different approaches to the computation of the moments of Jacobi Polynomials with non classical parameters of the form $\alpha_m=m+1/2$, $\beta_m=-m-1/2$. Both of them start from defining the weight function $w(z, \alpha_m, \beta_n)=(1-x)^{\alpha_m}(1+x)^{\beta_m}$ continuously in a contour $\Gamma$ on a Riemann Surface. The first approach is an explicit computation by parametrizing $\Gamma$, and the second is by using residues on a closed curve obtained by deforming the contour $\Gamma$ and performing a change of variables. This problems appeared in the search for the definite integral of the negative power of a quartic polynomial.


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Patrick Njionou Sadjang, Wolfram A. Koepf and Mama Foupouagnigni, On Moments of Classical Orthogonal Polynomials, J. Mat Anal. Appl. 424. (2015) 122-151. no 1, 122151.

Joint work with Victor Moll (Tulane University, US) and Kenneth McLaughlin (Tulane University, US).

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