منابع مشابه
On q-summation and confluence
This paper is divided in two parts. In the first part we consider a convergent q-analog of the divergent Euler series, with q ∈ (0, 1), and we show how the Borel sum of a generic Gevrey formal solution to a differential equation can be uniformly approximated on a convenient sector by a meromorphic solution of a corresponding q-difference equation. In the second part, we work under the assumptio...
متن کاملOn q-Operators and Summation of Some q-Series
Using Jackson's q-derivative and the q-Stirling numbers, we establish some transformation theorems leading to the values of some convergent q-series.
متن کاملSOME CURIOUS q-SUMMATION FORMULAE
We derive a new general transformation for WP-Bailey pairs by considering the a certain limiting case of a WP-Bailey chain previously found by the authors, and examine several consequences of this new transformation. These consequences include new summation formulae involving WP-Bailey pairs. Another consequence is a rather unusual summation formulae in which one side is an infinite basic-hyper...
متن کاملNew Proofs of Some q-Summation and q-Transformation Formulas
We obtain an expectation formula and give the probabilistic proofs of some summation and transformation formulas of q-series based on our expectation formula. Although these formulas in themselves are not the probability results, the proofs given are based on probabilistic concepts.
متن کاملq–GAUSS SUMMATION VIA RAMANUJAN AND COMBINATORICS
where |c/(ab)| < 1. Gauss’s name is attached to this theorem, because it is the qanalogue of Gauss’s summation for ordinary or Gaussian hypergeometric series. The theorem (1.1) was however first discovered by E. Heine [8] in 1847. We only know of two proofs of (1.1) up to recent times. The first proof, due to Heine [8], uses what we now call Heine’s transformation, and this proof can be found i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 2009
ISSN: 0373-0956,1777-5310
DOI: 10.5802/aif.2433