Jang Soo Kim (김장수), Combinatorics of continued fractions and its application to Jacobi’s triple product identity

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.