scholarly journals A product integral representation for an evolution system

1971 ◽  
Vol 27 (3) ◽  
pp. 549-549 ◽  
Author(s):  
J. V. Herod
Keyword(s):  
Integral Representation ◽  
Evolution System ◽  
Product Integral

The product integral

1991 ◽  
Vol 55 (5) ◽  
pp. 2042-2076 ◽  
Author(s):  
O. V. Manturov
Keyword(s):  
Product Integral

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

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 984
Author(s):  
Pedro J. Miana ◽  
Natalia Romero
Keyword(s):  
Integral Representation ◽  
Special Functions ◽  
Laguerre Polynomials ◽  
Function Spaces ◽  
Laguerre Functions ◽  
Addition Formula ◽  
Lebesgue Spaces ◽  
Rodrigues Formula ◽  
Generalized Laguerre Polynomials ◽  
New Family

Generalized Laguerre polynomials, Ln(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.

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