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A Family of Combinatorial Identities
Published online by Cambridge University Press: 20 November 2018
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In a recent paper, Murray Eden [5] generalized the simple identity for the Eulerian product,
1.1
and obtained the following infinite family of identities:
For A= 1,2, 3,…, let
1.2
where we assume throughout that |x| < 1, empty products equal unity and empty sums equal zero; then
1.3
As Eden noted, Fh(b;x) is the generating function of ph(m, n) which denotes the number of partitions of n into m parts, in which the largest part appears exactly h times and all other parts are distinct:
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