Hausdorff dimensions in Engel expansions

q–ENGEL SERIES EXPANSIONS AND SLATER’S IDENTITIES

We describe the q–Engel series expansion for Laurent series discovered by John Knopfmacher and use this algorithm to shed new light on partition identities related to two entries from Slater’s list. In our study Al-Salam/Ismail and Santos polynomials play a crucial rôle. Dedicated to the memory of John Knopfmacher 1937–1999

Engel Series and Cohen-Egyptian Fraction Expansions

Recommended by Stéphane Louboutin Two kinds of series representations, referred to as the Engel series and the Cohen-Egyptian fraction expansions, of elements in two different fields, namely, the real number and the discrete-valued non-archimedean fields are constructed. Both representations are shown to be identical in all cases except the case of real rational numbers.

An Innnite Family of Engel Expansions of Rogers-ramanujan Type

The Extended Engel Expansion is an algorithm that leads to unique series expansions of q-series. Various examples related to classical partition theorems, including the RogersRamanujan identities, have been given recently. The object of this paper is to show that the new and elegant Rogers-Ramanujan generalization found by Garrett, Ismail, and Stanton also ts into this framework. This not only ...

Metric Properties of Engel Series Expansions of Laurent Series

Engel Expansions of q-Series by Computer Algebra

The q-Engel Expansion is an algorithm that leads to unique series expansions of qseries. Various examples related to classical partition theorems, including the RogersRamanujan identities together with the elegant generalization found by Garrett, Ismail and Stanton, have been described recently. The object of this paper is to present the computer algebra package Engel, written in Mathematica, t...