Combinatorics of continued fractions and its application to Jacobi’s triple product identity

Jang Soo Kim

KIAS

KIAS

2013/09/25 Wed 4PM-5PM

ROOM 1409

ROOM 1409

In this talk we will see a combinatorial way to expand certain continued fractions using lattice paths called Motzkin paths. This method allows us to prove a formula for q-secant numbers. I will explain that this approach can be used to find a finite version of Jacobi’s triple product identity. This talk is based on my paper with Matthieu Josuat-Vergès: “Touchard-Riordan formulas, T-fractions, and Jacobi’s triple product identity”, The Ramanujan Journal, Volume 30, Issue 3, pp 341-378.

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