q-Apery Irrationality Proofs by q-WZ Pairs
نویسندگان
چکیده
w x Ž . In 1948, Paul Erdos E1 proved the irrationality of h 1 . Recently, ̋ 2 w x Peter Borwein used Pade approximation techniques B1 and some coḿ w x Ž . plex analysis methods B2 to prove the irrationality of both h 1 and q Ž . Ln 2 . Here we present a proof in the spirit of Apery’s magnificent proof ́ q Ž . w x of the irrationality of z 3 A , which was later delightfully accounted by w x Alf van der Poorten P . This method of proof gives favorable irrationality Ž . Ž . Ž . measure s 4.80 for Ln 2 compared to the irrationality measure s 54.0 q w x implied in B1, B2 . Further discussion of irrationality results for certain w x series is to be found in Erdos E2 . ̋
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