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We prove the existence of a transmutation operator between two weighted Sturm-Liouville operators. We also provide an explicit formula for the transmutation operator and a construction algorithm. An example and an application to an inverse spectral problem are also considered. 1991 Mathematics Subject Classification. 34A25, 34A55, 44A05.doi:10.1063/1.1758321 fatcat:3p5uhdjumrcdfhmm3lvpj5rm4u