Yu-Tian Li

collaborators

3 papers

math.CA2026

The Koornwinder--Kostenko--Teschl Conjecture for Jacobi Polynomials and the Discrete Laguerre Phase Transition

Yu-Tian Li

We prove the refined Koornwinder--Kostenko--Teschl conjecture. For the normalized weighted Jacobi function and all $n \in N_0$ , $α, β \geq 0$ , and $- 1 \leq x \leq 1$ , $$ |g\_n^{(α,β)…

math.CA2026

The Erdélyi--Magnus--Nevai and Krasikov Conjectures for Jacobi Polynomials

Qi-Feng Bai, Yu-Tian Li

Let $p_{n}^{(α, β)}$ denote the Jacobi polynomial orthonormal for the weight $(1 - x)^{α} (1 + x)^{β}$ on $[- 1, 1]$ , where $α, β \geq - 1/2$ , and put $S = α + β + 1$ . We prove the uniform degree--paramete…

math.CA2026

Airy Turning-Point Asymptotics for Ramanujan's Entire Function $A_{q} (z)$

Yu-Tian Li

Let $A_{q} (z) = k = 0 \sum \infty \frac{q ^{k^{2}}}{( q ; q ) _{k}} (- z)^{k}$ be Ramanujan's entire function. We study it in the turning-point scaling $$ q=e^{-\varepsilon},\qquad z=\frac{\sqr…

The Koornwinder--Kostenko--Teschl Conjecture for Jacobi Polynomials and the Discrete Laguerre Phase Transition

The Erdélyi--Magnus--Nevai and Krasikov Conjectures for Jacobi Polynomials

Airy Turning-Point Asymptotics for Ramanujan's Entire Function Aq​(z)

Airy Turning-Point Asymptotics for Ramanujan's Entire Function $A_{q} (z)$