Explicit matrix inverses for lower triangular matrices with entries involving continuous q-ultraspherical polynomials
نویسندگان
چکیده
منابع مشابه
Explicit matrix inverses for lower triangular matrices with entries involving Jacobi polynomials
For a two-parameter family of lower triangular matrices with entries involving Jacobi polynomials an explicit inverse is given, with entries involving a sum of two Jacobi polynomials. The formula simplifies in the Gegenbauer case and then one choice of the parameter solves an open problem in a recent paper by Koelink, van Pruijssen & Román. The twoparameter family is closely related to two two-...
متن کاملOn Inverses of Triangular Matrices with Monotone Entries
This note employs recurrence techniques to obtain entry-wise optimal inequalities for inverses of triangular matrices whose entries satisfy some monotonicity constraints. The derived bounds are easily computable.
متن کاملA second addition formula for continuous q-ultraspherical polynomials
This paper provides the details of Remark 5.4 in the author’s paper “Askey-Wilson polynomials as zonal spherical functions on the SU(2) quantum group”, SIAM J. Math. Anal. 24 (1993), 795–813. In formula (5.9) of the 1993 paper a two-parameter class of Askey-Wilson polynomials was expanded as a finite Fourier series with a product of two 3phi2’s as Fourier coefficients. The proof given there use...
متن کاملBounds for Inverses of Triangular Toeplitz Matrices
This short note provides an improvement on a recent result of Vecchio on a norm bound for the inverse of a lower triangular Toeplitz matrix with nonnegative entries. A sharper asymptotic bound is obtained as well as a version for matrices of finite order. The results are shown to be nearly best possible under the given constraints. 1. Introduction. This paper provides an improvement on a recent...
متن کاملExplicit Formulas Involving q-Euler Numbers and Polynomials
and Applied Analysis 3 Similarly, the q-Bernoulli polynomials and numbers with weight 0 are defined, respectively, as B̃n,q x lim n→∞ 1 [ pn ] q pn−1 ∑ y 0 ( x y )n q
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2015
ISSN: 0021-9045
DOI: 10.1016/j.jat.2015.06.004