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A Connection Problem for Second Order Linear Differential Equations with Two Irregular Singular Points

1976; Society for Industrial and Applied Mathematics; Volume: 7; Issue: 2 Linguagem: Inglês

10.1137/0507013

1095-7154

F. Naundorf,

Spectral Theory in Mathematical Physics

Next article A Connection Problem for Second Order Linear Differential Equations with Two Irregular Singular PointsFriedrich NaundorfFriedrich Naundorfhttps://doi.org/10.1137/0507013PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractUsing Heaviside’s exponential series, a power series solution of the differential equation is split into formal solutions with known asymptotic expansions.[1] M. Abramowitz and , I. A. Stegun, Handbook of Mathematical Functions, Dover, New York, 1965 Google Scholar[2] E. W. Barnes, On functions defined by simple types of hypergeometric series, Trans. Cambridge Philos. Soc., 20 (1906), 253–279 Google Scholar[3] Ludwig Bieberbach, Theorie der gewöhnlichen Differentialgleichungen auf funktionentheoretischer Grundlage dargestellt, Zweite umgearbeitete und erweiterte Auflage. 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Watson, A Course of Modern Analysis, Cambridge University Press, Cambridge, England, 1969 Google Scholar Next article FiguresRelatedReferencesCited byDetails Sextic anharmonic oscillators and Heun differential equations20 July 2022 | The European Physical Journal Plus, Vol. 137, No. 7 Cross Ref A new approach for the study of limit cyclesJournal of Differential Equations, Vol. 269, No. 7 Cross Ref Global solutions of the biconfluent Heun equation7 July 2015 | Numerical Algorithms, Vol. 71, No. 4 Cross Ref Scattering by infinitely rising one-dimensional potentialsAnnals of Physics, Vol. 363 Cross Ref Global solution of the cubic oscillator30 September 2014 | Journal of Physics A: Mathematical and Theoretical, Vol. 47, No. 41 Cross Ref Spiked oscillators: exact solution4 August 2010 | Journal of Physics A: Mathematical and Theoretical, Vol. 43, No. 38 Cross Ref An algorithm to obtain global solutions of the double confluent Heun equation14 May 2008 | Numerical Algorithms, Vol. 49, No. 1-4 Cross Ref Connection factors in the Schrödinger equation with a polynomial potentialJournal of Computational and Applied Mathematics, Vol. 207, No. 2 Cross Ref Quantum anharmonic oscillators: a new approach22 March 2005 | Journal of Physics A: Mathematical and General, Vol. 38, No. 14 Cross Ref Bound states and resonances in sombrero potentialsPhysics Letters A, Vol. 286, No. 6 Cross Ref Second-order linear differential equations with two irregular singular points of rank three: the characteristic exponentJournal of Computational and Applied Mathematics, Vol. 118, No. 1-2 Cross Ref Bound states and “resonances” in quantum anharmonic oscillatorsPhysics Letters A, Vol. 270, No. 1-2 Cross Ref On the Central Connection Problem for the Double Confluent Heun Equation19 November 2010 | Mathematische Nachrichten, Vol. 195, No. 1 Cross Ref On the central connection problem for equations with an irregular singular point of a single levelJournal of Dynamical and Control Systems, Vol. 3, No. 1 Cross Ref A new approach to the spherical Stark problem in hydrogenPhysics Letters A, Vol. 219, No. 3-4 Cross Ref Ein Verfahren zur Lösung des Zusammenhangproblems bei linearen Differentialgleichungen zweiter Ordnung mit mehreren singulären StellenZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 59, No. 6 Cross Ref A method for computing scattering phase shifts and eigenvalues of the Schrödinger equation with singular potentialsJournal of Mathematical Physics, Vol. 19, No. 6 Cross Ref Ein Verfahren zur Berechnung der charakteristischen Exponenten von linearen Differentialgleichungen zweiter Ordnung mit zwei stark singulären StellenZAMM - Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 57, No. 1 Cross Ref Volume 7, Issue 2| 1976SIAM Journal on Mathematical Analysis History Submitted:30 July 1974Published online:17 February 2012 InformationCopyright © 1976 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0507013Article page range:pp. 157-175ISSN (print):0036-1410ISSN (online):1095-7154Publisher:Society for Industrial and Applied Mathematics