Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 212, pp. 116.
A matrix formulation of Frobenius power series solutions using products
of
matrices
Jeremy Mandelkern
Abstract:
In Coddington and Levison [7, p. 119, Thm. 4.1] and
Balser [4, p. 1819, Thm. 5], matrix formulations of Frobenius
theory, near a regular singular point, are given using
matrix
recurrence relations yielding fundamental matrices consisting of two
linearly independent solutions together with their quasiderivatives.
In this article we apply a reformulation of these matrix methods to the
Bessel equation of nonintegral order. The reformulated approach of this
article differs from [7] and [4] by its
implementation of a new ``vectorization'' procedure that yields recurrence
relations of an altogether different form: namely, it replaces the implicit
matrix recurrence relations of both [7] and
[4] by explicit
matrix recurrence relations
that are implemented by means only of
matrix products.
This new idea of using a vectorization procedure may further enable the
development of symbolic manipulator programs for matrix forms of the
Frobenius theory.
Submitted January 12, 2015. Published August 17, 2015.
Math Subject Classifications: 34B30, 33C10, 68W30, 3403, 01A55.
Key Words: Matrix power series; Frobenius theory; Bessel equation.
An addendum was posted on May 11, 2017, It modifies two matrices
from Section 7. See the last page of this article.
Show me the PDF file (284 KB),
TEX file, and other files for this article.

Jeremy Mandelkern
Department of Mathematics
Eastern Florida State College
Melbourne, FL 32935, USA
email: mandelkernj@easternflorida.edu

Return to the EJDE web page