Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces

Pedro J. Miana and Natalia Romero
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Pedro J. Miana: Departamento de Matemáticas, Facultad de Ciencias & IUMA, Universidad de Zaragoza, 50009 Zaragoza, Spain
Natalia Romero: Departamento de Matemáticas y Computación, Facultad de Ciencia y Tecnología, Universidad de La Rioja, 26006 Logroño, Spain

Mathematics, 2021, vol. 9, issue 9, 1-15

Abstract: Generalized Laguerre polynomials, L n ( ? ) , verify the well-known Rodrigues’ formula. Using Weyl and Riemann–Liouville fractional calculi, we present several fractional generalizations of Rodrigues’ formula for generalized Laguerre functions and polynomials. As a consequence, we give a new addition formula and an integral representation for these polynomials. Finally, we introduce a new family of fractional Lebesgue spaces and show that some of these special functions belong to them.

Keywords: Rodrigues’ formula; Laguerre functions; function spaces; fractional calculus (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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