most recent 30 from http://mathoverflow.net 2013-05-23T00:00:57Z http://mathoverflow.net/feeds/question/68206 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/68206/closure-properties-of-q-differential-equations Martin Rubey 2011-06-19T09:47:03Z 2011-06-19T09:47:03Z

<p>I am interested in q-differential equations of the form</p> <p>$p(f(z), f(qz),\dots,f(q^kz))=0$</p> <p>where $p$ is a polynomial and $k$ an nonnegative integer. I wonder about the closure properties of the class of (formal) powers series satisfying such an equation. A bit is known when $p$ is required to be linear, see Section 3 of "A Mathematica package for q-holonomic sequences and power series" by Manuel Kauers and Christoph Koutschan.</p> <p>In particular, if $f$ and $g$ satisfy a $q$-ADE, do $f+g$, $f\cdot g$ and $f\circ h$ for suitably simple $h$, too? And if so, what is the $k$ in the resulting equations?</p>