Arithmetische Eigenschaften spezieller Heinescher Reihen

On approximation measures of q-logarithms

“…With this choice of n we have a contradiction in (15). This implies (12) and thus again (14) is true. Taking logarithms in (14) and using the assumptions of our theorem we obtain…”

“…We now prove that with a suitable choice of n T. Matala-Aho and K. Vaananen [12] Then, by the product formula and the estimates of our theorem,…”

“…The present work considers irrationality measures of the values of the g-logarithm The arithmetic properties of the values of these and related functions are considered recently in a series of papers [1,3,4,5,6,7,9,10,11,12,13]. Here we are able to improve the earlier irrationality measures both in the Archimedean and p-adic case.…”

On Arithmetical Properties of Certain q-Series

“…In the following we shall compute second type Padè approximations for the functions (see for example [6,10] for details)…”

“…The reason being that limiting the considerations only to the "relevant" cases does not essentially either shorten or simplify the computations, Properties of Certain q-Series 133 especially since Theorem 1 is given in general form. Also, the corresponding result of Lemma 2 in[6] (or[10]) does not cover, at least directly the Heine series, and hence some explanations are needed.Theorem 1. When the conditions (5),(6) and(7)are satisfied, then there exist positive constants C, E and H 0 such that…”