K. Castillo

activity

20172026

collaborators

9 papers

math.CA2026

Elementary ratio and zero limits for varying recurrences

K. Castillo, S. Yakubovich

Two theorems of Loureiro and Van Assche on ratio and zero limits provided part of the motivation for this note. Their elementary nature permits direct proofs; Appendix B gives comp…

math.CA2026

Complete Bernstein functions and scaled ultraspherical zeros

K. Castillo

Let $z_{n, j} (λ)$ denote the positive zeros, in decreasing order, of the ultraspherical polynomial $C_{n}^{λ}$ , $λ > - 1/2$ , with the reduced limiting interpretation at $λ = 0$ specified bel…

math.CA2026

Equal-Phase Monotonicity for Weighted Jacobi-Radau Functions and Jacobi Lebesgue Constants

K. Castillo, P. -C. Hang

For the Jacobi family with parameters $(0, β)$ , $β \geq - 1/3$ , we prove a continuous comparison theorem for the associated weighted Jacobi--Radau functions. When two consecutive funct…

math.CA2026

A proof of Askey's convexity conjecture

K. Castillo, S. Yakubovich

For $- 1 < α \leq 1/2$ , let $J_{α}$ be the Bessel function of the first kind and let $j_{α, 2}$ be its second positive zero. Define $β (α) < α + 1$ by $$ \int_0^{j_{α,2}}u^{-β(α)}J_α(u)\,du=0.…

math.CA2026

A proof of Gautschi's conjecture on subrange Jacobi polynomials

V. Botta, K. Castillo, L. Tertuliano da Silva

Let $π_{n}$ be the monic polynomial of degree $n$ orthogonal on $[- c, c]$ , $0 < c \leq 1$ , with respect to the Jacobi weight $(1 - x)^{α} (1 + x)^{β}$ , where $- 1 < α < β$ . Gautschi conjectured that \[…

math.CA2026

A solution to Meneguette's polynomial problem

K. Castillo

In 1979, Jeltsch [Numer. Math. 32 (1979), 167-181] conjectured that every zero-stable Brown method is stiffly stable. For Brown $(K, L)$ methods, Meneguette subsequently reduced the…