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- Title
Fractional Generalizations of Rodrigues-Type Formulas for Laguerre Functions in Function Spaces.
- Authors
Miana, Pedro J.; Romero, Natalia; Hartung, Ferenc
- Abstract
Generalized Laguerre polynomials, L n (α) , 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.
- Subjects
FUNCTION spaces; LAGUERRE polynomials; FRACTIONAL calculus; GENERALIZATION
- Publication
Mathematics (2227-7390), 2021, Vol 9, Issue 9, p984
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math9090984