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ERY IRRATIONALITY PROOFS BY qWZ PAIRS Tewodros Amdeberhan and Doron Zeilberger
 

Summary: q­AP '
ERY IRRATIONALITY PROOFS BY q­WZ PAIRS
Tewodros Amdeberhan and Doron Zeilberger
Department of Mathematics, Temple University, Philadelphia PA 19122, USA
tewodros@math.temple.edu, zeilberg@math.temple.edu
Abstract. Using WZ pairs, Ap'ery­style proofs of the irrationality of the q­analogues of the Harmonic series
and Ln(2) are given. For the q­analogue of Ln(2), this method produces an improved irrationality measure.
0. Introduction:
Let us define the following q­analogues of the Harmonic series
P 1
n=1
1
n and Ln(2), respectively by:
h q (1) : =
1
X
k=1
1
q k \Gamma 1 (for jqj ? 1),
(0.1)

  

Source: Amdeberhan, Tewodros - Department of Mathematics, Tulane University

 

Collections: Mathematics