A Family of Combinatorial Identities
Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 11-18
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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, F h (b;x) is the generating function of p h (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:
Andrews, G. E.; Subbarao, M. V.; Vidyasagar, M. A Family of Combinatorial Identities. Canadian mathematical bulletin, Tome 15 (1972) no. 1, pp. 11-18. doi: 10.4153/CMB-1972-003-1
@article{10_4153_CMB_1972_003_1,
author = {Andrews, G. E. and Subbarao, M. V. and Vidyasagar, M.},
title = {A {Family} of {Combinatorial} {Identities}},
journal = {Canadian mathematical bulletin},
pages = {11--18},
year = {1972},
volume = {15},
number = {1},
doi = {10.4153/CMB-1972-003-1},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-003-1/}
}
TY - JOUR AU - Andrews, G. E. AU - Subbarao, M. V. AU - Vidyasagar, M. TI - A Family of Combinatorial Identities JO - Canadian mathematical bulletin PY - 1972 SP - 11 EP - 18 VL - 15 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1972-003-1/ DO - 10.4153/CMB-1972-003-1 ID - 10_4153_CMB_1972_003_1 ER -
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