Convergence of Padé approximants of partial theta functions and the Rogers-Szegö polynomials

DOI10.1007/BF01890574zbMath0634.41013MaRDI QIDQ1096820

Doron S. Lubinsky, Edward B. Saff

Publication date: 1987

Published in: Constructive Approximation (Search for Journal in Brave)

zbMATH Keywords

partial theta functionsequences of Padé approximantszero distribution of the Rogers-Szegö polynomials

Mathematics Subject Classification ID

Approximation by rational functions (41A20)

Related Items (30)

Metric density results for the value distribution of Sudler products ⋮ Convergence of Padé approximants for a \(q\)-hypergeometric series (Wynn's power series III) ⋮ Toeplitz matrix techniques and convergence of complex weight Padé approximants ⋮ Uniform convergence of rows of the Padé table for functions with smooth Maclaurin series coefficients ⋮ Rate of convergence of Padé approximants for a particular Wynn series ⋮ Reflections on the Baker–Gammel–Wills (Padé) Conjecture ⋮ Padé tables of entire functions of very slow and smooth growth. II ⋮ The convergence of diagonal Padé approximants and the Padé conjecture ⋮ On extreme values for the Sudler product of quadratic irrationals ⋮ On Weyl products and uniform distribution modulo one ⋮ On the order of magnitude of Sudler products ⋮ A domain free of the zeros of the partial theta function ⋮ Operator identities involving the bivariate Rogers-Szegö polynomials and their applications to the multiple \(q\)-series identities ⋮ An explicit example of polynomials orthogonal on the unit circle with a dense point spectrum generated by a geometric distribution ⋮ Explicit construction of multivariate Padé approximants for a \(q\)-logarithm function ⋮ Convergence of Padé approximants for a \(q\)-hypergeometric series (Wynn's power series I) ⋮ Growth of the Sudler product of sines at the golden rotation number ⋮ Irregular distribution of \(\{n\beta{}\} \), \(n=1,2,3,\)\dots , quadrature of singular integrands, and curious basic hypergeometric series ⋮ BILATERAL BAILEY LEMMA AND FALSE THETA FUNCTIONS ⋮ Convergence of simultaneous Hermite-Padé approximants to the \(n\)-tuple of \(q\)-hypergeometric series \(\{_ 1\Phi_ 1 (_{c,\gamma_ j}^{(1,1)};z)\}_{j=1}^ n\) ⋮ Multivariate Padé approximants to a meromorphic function ⋮ General order multivariate Padé approximants for pseudo-multivariate functions ⋮ Multivariate Padé approximants associated with functional relations ⋮ Rows and diagonals of the Walsh array for entire functions with smooth Maclaurin series coefficients ⋮ On the irrationality of \(\sum \frac{t^n} {A\alpha^n+ B\beta^n}\) ⋮ Quadrature formulas associated with Rogers-Szegő polynomials ⋮ On uniform convergence of rational, Newton-Padé interpolants of type (n,n) with free poles as \(n\to \infty\) ⋮ The size of \((q;q)_n\) for \(q\) on the unit circle ⋮ Matrix models and stochastic growth in Donaldson-Thomas theory ⋮ Convergence of simultaneous Hermite-Padé approximants to the \(n\)-tuple of \(q\)-hypergeometric series \(\{_ 2\Phi_ 0((A,\alpha_ j), (1,1);z)\}_{j=1}^ n\)

Cites Work

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