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5 papers · 1 filter
On the norms and roots of orthogonal polynomials in the plane and -optimal polynomials with respect to varying weights
F. Balogh, M. Bertola
For a measure on a subset of the complex plane we consider -optimal weighted polynomials, namely, monic polynomials of degree with a varying weight of the form $w^n = {\rm…
Total integrals of global solutions to Painleve II
Jinho Baik, Robert Buckingham, Jeffery DiFranco +1
We evaluate the total integral from negative infinity to positive infinity of all global solutions to the Painleve II equation on the real line. The method is based on the interpla…
Generalized Bochner theorem: characterization of the Askey-Wilson polynomials
Luc Vinet, Alexei Zhedanov
Assume that there is a set of monic polynomials satisfying the second-order difference equation $$ A(s) P_n(z(s+1)) + B(s) P_n(z(s)) + C(s) P_n(z(s-1)) = λ_n P_n(z(s)), n=…
The Stokes phenomenon in the confluence of the hypergeometric equation using Riccati equation
Caroline Lambert, Christiane Rousseau
In this paper we study the confluence of two regular singular points of the hypergeometric equation into an irregular one. We study the consequence of the divergence of solutions a…
Elliptic Biorthogonal Polynomials Connected with Hermite's Continued Fraction
Luc Vinet, Alexei Zhedanov
We study a family of the Laurent biorthogonal polynomials arising from the Hermite continued fraction for a ratio of two complete elliptic integrals. Recurrence coefficients, expli…