An Extension of a Formula of F. S. Rofe-Beketov

Fritz Gesztesy () and Roger Nichols
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Fritz Gesztesy: Department of Mathematics, Baylor University, Sid Richardson Bldg., 1410 S. 4th Street, Waco, TX 76706, USA
Roger Nichols: Department of Mathematics, The University of Tennessee at Chattanooga, 615 McCallie Avenue (Dept. 6956), Chattanooga, TN 37403, USA

Mathematics, 2025, vol. 13, issue 3, 1-14

Abstract: We address the following problem in this study: given a nontrivial solution, y 1 , of a four-coefficient Sturm–Liouville eigenvalue differential equation, construct a second solution, y 2 , linearly independent of y 1 . In the process of describing the solution of this problem, we review the approaches by d’Alembert and Rofe-Beketov in the case of three-coefficient Sturm–Liouville eigenvalue differential equations.

Keywords: Sturm–Liouville operator; distributional coefficient; d’Alembert and Rofe-Beketov’s formulas (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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