A thirdorder Aperylike recursion for $\zeta(5)$
Abstract
In 1978, Apery has given sequences of rational approximations to $\zeta(2)$ and $\zeta(3)$ yielding the irrationality of each of these numbers. One of the key ingredient of Apery's proof are secondorder difference equations with polynomial coefficients satisfied by numerators and denominators of the above approximations. Recently, a similar secondorder difference equation for $\zeta(4)$ has been discovered. The note contains a possible generalization of the above results for the number $\zeta(5)$.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2002
 arXiv:
 arXiv:math/0206178
 Bibcode:
 2002math......6178Z
 Keywords:

 Mathematics  Number Theory;
 Mathematics  Classical Analysis and ODEs;
 Primary 11Y60;
 Secondary 11J20;
 33C20
 EPrint:
 5 pages, AmSTeX