Fractional operators and special functions. I. Bessel functions

Details Fractional operators and special functions. I. Bessel functions Fractional operators and special functions. I. Bessel functions

2002-12-04

arxiv.org/abs/math-ph/0212018v1

Physics

Mathematical Physics

15 pages, Latex2e

Scientific paper

10.1063/1.1561593

Most of the special functions of mathematical physics are connected with the representation of Lie groups. The action of elements $D$ of the associated Lie algebras as linear differential operators gives relations among the functions in a class, for example, their differential recurrence relations. In this paper, we define fractional generalizations $D^\mu$ of these operators in the context of Lie theory, determine their formal properties, and illustrate their use in obtaining interesting relations among the functions. We restrict our attention here to the Euclidean group E(2) and the Bessel functions. We show that the two-variable fractional operator relations lead directly to integral representations for the Bessel functions, reproduce known fractional integrals for those functions when reduced to one variable, and contribute to a coherent understanding of the connection of many properties of the functions to the underlying group structure. We extend the analysis to the associated Legendre functions in a following paper.

Affiliated with

Also associated with

No associations

Rating

Fractional operators and special functions. I. Bessel functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Fractional operators and special functions. I. Bessel functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Fractional operators and special functions. I. Bessel functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-702992