[seqfan] Re: Cassini transformation of linear recursion of order 3

mathar mathar at mpia-hd.mpg.de
Wed Mar 6 10:15:36 CET 2013


In answer to http://list.seqfan.eu/pipermail/seqfan/2013-March/010894.html

Vladmir Shevelev wrote:
vs> recurrence of order R(N) with constant coefficients for
vs> g=a^2(n)-a(n-1)*a(n+1), if a(n) satisfies a linear  recursion of order
vs> N with constant coefficients. Thus my result yields that R(3)=3. I think
vs> that even function R(N) is unknown and it is, in my opinion,  an
vs> important conctete open problem.

See for example

@article{RabinowitzFQ,
author = {S. Rabinowitz},
title = {Algorithmic manipulation of third-order linear recurrences},
url={http://www.mathpropress.com/stan/bibliography/algorithmic3rdOrder.pdf},
journal={Fib. Quart.},
volume=35,
number=5,
pages={447--464},
mrnumber={1416685 (97g:11009)},
year = 1996}

@article{HounkonnouApplMath29,
author = {Mahouton Norbert Hounkonnou and Said Belmehdi and Andr\'e Ronveaux},
title = {Linearization of arbitrary products of classical orthogonal polynomials},
journal = {Applic.\ Mathemat.},
volume = 27,
number = 2,
pages = {187--196},
year = 2000}

Richard J. Mathar



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