Infinite product representation of solution of indefinite Sturm-Liouville problem

AuthorsSeyfollah Mosazadeh
JournalIranian Journal of Mathematical Chemistry
Presented by‎University of Kashan
Paper TypeFull Paper
Published At2013
Journal GradeScientific - research
Journal TypeTypographic
Journal CountryIran, Islamic Republic Of
Journal IndexISI, ISC


In this paper, we investigate infinite product representation of the solution of a Sturm- Liouville equation with an indefinite weight function which has two zeros and/or singularities in a finite interval. First, by using of the asymptotic estimates provided in [W. Eberhard, G. Freiling, K. Wilcken-Stoeber, Indefinite eigenvalue problems with several singular points and turning points, Math. Nachr. 229, 51-71 (2001)] for a special fundamental system of the solutions of Sturm-Liouville equation, we obtain the asymptotic behavior of it’s solutions and eigenvalues, then we obtain the infinite product representation of solution of the equation