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

Mathematics

Natalia Romero¹  PedroJ. Miana² 

[1] Departamento de Matemáticas y Computación, Facultad de Ciencia y Tecnología, Universidad de La Rioja, 26006 Logron˜o, Spain;Departamento de Matemáticas, Facultad de Ciencias & IUMA, Universidad de Zaragoza, 50009 Zaragoza, Spain;

关键词: Rodrigues’ formula;    Laguerre functions;    function spaces;    fractional calculus;   

DOI  :  10.3390/math9090984

来源: DOAJ

【 摘 要 】

Generalized Laguerre polynomials, $L_n^{\left(\alpha \right)}$, 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.

【 授权许可】

Unknown