Number Theory Seminar
Speaker: Lin Jiu
Title: “Orthogonal Polynomials for Bernoulli and Euler Polynomials”
Abstract: Recent results interpret Bernoulli and Euler polynomials as moments of certain random variables. Then, it is natural to consider the corresponding orthogonal polynomials. On the other hand, a general connection between moments of random variables and the generalized Motzkin numbers, via continued fractions, reveals that the orthogonal polynomials, especially their three-term recurrences, endow the Bernoulli and Euler polynomials with combinatorial interpretations as weighted lattice paths. It will be shown that the orthogonal polynomials with respect to Bernoulli polynomials are the continuous Hahn polynomials and those with respect to Euler polynomials are Meixner-Pollaczek polynomials. A generalization on the Euler polynomials of higher order is obtained; while for the Bernoulli polynomials of higher order, a conjecture will be shown.
This is joint work with Diane Shi.
Chase Building, Room 319