On a gap theorem of fabry's type for classical orthogonal series

Abstract

We deal with seires of the form , where the functions , represent the so called generalized classical orthogonal polynomials, that is Jacobi , Laguerre , and Hermite(H_n (z)) polynomials with parameters . It is a well known fact that these calssical orthogonal series fulfill a gap theorem of Hadamard's type. In the following we will show that it is also possible to derive a gap theorem of Fabry's type in a unified approach for all three kinds of orthogonal series, using certain differential operators and the validity of Hadamard's gap theorem.

Keywords:

• Hadamard's gap theorem
• orthogonal series
• differential operators

MSC(1991):

• 33C45

Additional information

Notes on contributors

Jutta Faldey