Heine, Hilbert, Pade, Riemann, and Stieltjes: a John Nuttall's work 25 years later

Details Heine, Hilbert, Pade, Riemann, and Stieltjes: a John Nuttall's work 25 years later Heine, Hilbert, Pade, Riemann, and Stieltjes: a John Nuttall's work 25 years later

2011-11-26

arxiv.org/abs/1111.6139v1

Mathematics

Classical Analysis and ODEs

29 pages, 6 figures, submitted to the Proceedings of the OPSFA Conference, dedicated to the 60th Birthday of Francisco (Paco)

Scientific paper

In 1986 J. Nuttall published in Constructive Approximation the paper "Asymptotics of generalized Jacobi polynomials", where with his usual insight he studied the behavior of the denominators ("generalized Jacobi polynomials") and the remainders of the Pade approximants to a special class of algebraic functions with 3 branch points. 25 years later we try to look at this problem from a modern perspective. On one hand, the generalized Jacobi polynomials constitute an instance of the so-called Heine-Stieltjes polynomials, i.e. they are solutions of linear ODE with polynomial coefficients. On the other, they satisfy complex orthogonality relations, and thus are suitable for the Riemann-Hilbert asymptotic analysis. Along with the names mentioned in the title, this paper features also a special appearance by Riemann surfaces, quadratic differentials, compact sets of minimal capacity, special functions and other characters.

Affiliated with

Also associated with

No associations

Rating

Heine, Hilbert, Pade, Riemann, and Stieltjes: a John Nuttall's work 25 years later does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Heine, Hilbert, Pade, Riemann, and Stieltjes: a John Nuttall's work 25 years later, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Heine, Hilbert, Pade, Riemann, and Stieltjes: a John Nuttall's work 25 years later will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-483468