Deprecated: $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372
A differential equation for orthogonal polynomials - MaRDI portal

A differential equation for orthogonal polynomials

From MaRDI portal
Publication:2646411

DOI10.1215/S0012-7094-39-00534-XzbMath0021.30802OpenAlexW2024472793WikidataQ115240292 ScholiaQ115240292MaRDI QIDQ2646411

J. A. Shohat

Publication date: 1939

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-39-00534-x




Related Items

The recurrence coefficients of the orthogonal polynomials with the weights $w_\alpha(x)= x^\alpha \exp(-x^3+tx)$ and $W_\alpha(x)=|x|^{2\alpha+1} \exp(-x^6+tx^2)$On semiclassical linear functionals of classs=2: classification and integral representationsExact solutions of a q -discrete second Painlevé equation from its iso-monodromy deformation problem: I. Rational solutionsPainlevé-type differential equations for the recurrence coefficients of semi-classical orthogonal polynomialsOn semiclassical linear functionals: Integral representationsA large family of semi-classical polynomials: The perturbed ChebyshevOn the classification of differential equations having orthogonal polynomial solutions. IIDie Orthogonalisierung von Polynomen bei ganzen rationalen GewichtsfunktionenProperties of generalized Freud polynomialsAsymptotic behaviours of \(q\)-orthogonal polynomials from a \(q\)-Riemann Hilbert problemIntegrable differential systems for deformed Laguerre–Hahn orthogonal polynomialsSeveral characterizations of third-degree semiclassical linear forms of class two appearing via cubic decompositionZeros of orthogonal polynomials generated by canonical perturbations of measuresCoherent pairs of moment functionals of the second kind and associated orthogonal polynomials and Sobolev orthogonal polynomialsAbout families of orthogonal polynomials satisfying Heun's differential equationFrom Standard Orthogonal Polynomials to Sobolev Orthogonal Polynomials: The Role of Semiclassical Linear FunctionalsOrthogonal and Multiple Orthogonal Polynomials, Random Matrices, and Painlevé EquationsOn polynomials associated with an Uvarov modification of a quartic potential Freud-like weightA generalized sextic Freud weightToda-type differential equations for the recurrence coefficients of orthogonal polynomials and Freud transformationA finite class of orthogonal functions generated by Routh–Romanovski polynomialsSemi-classical linear functionals of class three: the symmetric caseStokes phenomena in discrete Painlevé IIElementary exact calculations of degree growth and entropy for discrete equationsOn regularity of semiclassical functionals of class (2,2)On the assignment of a Dirac-mass for a regular and semi-classical formOn semiclassical orthogonal polynomials via polynomial mappingsq-Discrete Painlevé equations for recurrence coefficients of modifiedq-Freud orthogonal polynomialsOn the Riemann-Hilbert problem for a \(q\)-difference Painlevé equationAsymptotics of determinants of Hankel matrices via non-linear difference equationsA Unified Description of the Asymmetric q-PV and d-PIV Equations and their Schlesinger TransformationsNewton sum rules of zeros of semiclassical orthogonal polynomialsRestoring discrete Painlevé equations from an E8(1)-associated oneA uniform asymptotic formula for orthogonal polynomials associated with \(\exp(-x^4)\)Characterizations of a special family of third-degree semi-classical forms of class oneÜber Differentialgleichungen für OrthogonalpolynomeVariations on a theme of Heine and Stieltjes: An electrostatic interpretation of the zeros of certain polynomialsOn certain properties of perturbed Freud-type weight: a revisitA family of nonlinear difference equations: existence, uniqueness, and asymptotic behavior of positive solutionsDiscrete semi-classical orthogonal polynominalsDiscretising the Painlevé equations à la Hirota-MickensSome perturbed sequences of order one of the Chebyshev polynomials of second kindPointwise asymptotics of the ratio of Jacobi-type polynomials