A closer look at some new identities

Geoffrey B. Campbell

International Journal of Mathematics and Mathematical Sciences, 1998, vol. 21, 1-6

Abstract:

We obtain infinite products related to the concept of visible from the origin point vectors. Among these is ∏ k = 3 ∞ ( 1 − Z ) φ , ( k ) / k = 1 1 − Z exp ( Z 3 2 ( 1 − Z ) 2 − 1 2 Z − 1 2 Z ( 1 − Z ) ) , | Z | < 1 , in which φ 3 ( k ) denotes for fixed k , the number of positive integer solutions of ( a , b , k ) = 1 where a < b < k , assuming ( a , b , k ) is the gcd ( a , b , k ) .

Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:289376

DOI: 10.1155/S0161171298000805

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