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q-AP ERY IRRATIONALITY PROOFS BY q-WZ PAIRS Tewodros Amdeberhan and Doron Zeilberger
 

Summary: q-AP ERY IRRATIONALITY PROOFS BY q-WZ 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 ery-styleproofs of the irrationalityof the q-analoguesof the Harmonic series
and Ln2 are given. For the q-analogue of Ln2, this method produces an improved irrationality measure.
0. Introduction:
Let us de ne the following q-analogues of the Harmonic series
P1
n=1
1
n and Ln2, respectively by:
hq1 : =
1X
k=1
1
qk , 1 for jqj 1,0.1
Lnq2 : =
1X
n=1

  

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

 

Collections: Mathematics