Explicit matrix inverses for lower triangular matrices with entries involving continuous q-ultraspherical polynomials
Copyright policy )Explicit matrix inverses for lower triangular matrices with entries involving continuous q-ultraspherical polynomials
For a one-parameter family of lower triangular matrices with entries involving continuous $q$-ultraspherical polynomials we give an explicit lower triangular inverse matrix, with entries involving again continuous $q$-ultraspherical functions. The matrices are $q$-analogues of results given by Cagliero and Koornwinder recently. The proofs are not $q$-analogues of the Cagliero-Koornwinder case, but are of a different nature involving $q$-Racah polynomials. Some applications of these new formulas are given. Also the limit $��\to 0$ is studied and gives rise to continuous $q$-Hermite polynomials for $0 < q < 1$ and $q > 1$.
10 pages, incorporating referee's comments
\(q\)-Racah polynomials, 33D15, 33D45, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Basic hypergeometric functions in one variable, \({}_r\phi_s\), Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, continuous \(q\)-ultraspherical polynomials, orthogonal polynomials, Mathematical Physics
\(q\)-Racah polynomials, 33D15, 33D45, Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Basic hypergeometric functions in one variable, \({}_r\phi_s\), Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, continuous \(q\)-ultraspherical polynomials, orthogonal polynomials, Mathematical Physics
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).4 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!