Irrationality proof of certain Lambert series using little q-Jacobi polynomials
| dc.creator | Coussement, Jonathan | |
| dc.creator | Smet, Christophe | |
| dc.date | 2007-01-12 | |
| dc.date.accessioned | 2026-07-07T07:40:37Z | |
| dc.date.available | 2026-07-07T07:40:37Z | |
| dc.description | We apply the Pade technique to find rational approximations to % \[h^{\pm}(q_1,q_2)=\sum_{k=1}^\infty\frac{\q_1^k}{1\pm \q_2^k}, 0<q_1,q_2<1, q_1\in\mathbb{Q}, q_2=1/p_2, p_2\in\mathbb{N}\setminus\{1\}.\] % A separate section is dedicated to the special case $q_i=q^{r_i}, r_i\in\mathbb{N}, q=1/p, p\in\mathbb{N}\setminus\{1\}$. In this construction we make use of little $q$-Jacobi polynomials. Our rational approximations are good enough to prove the irrationality of $h^{\pm}(q_1,q_2)$ and give an upper bound for the irrationality measure. | |
| dc.description | 16 pages | |
| dc.identifier | https://arxiv.org/abs/math/0701345 | |
| dc.identifier | http://arxiv.org/abs/math/0701345 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/121830 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | Number Theory | |
| dc.subject | 11J72 (Primary) 11J82, 33D45 (Secondary) | |
| dc.title | Irrationality proof of certain Lambert series using little q-Jacobi polynomials | |
| dc.type | text |