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A simple proof of the quintuple product identity
Authors:
L. Carlitz and M. V. Subbarao
Journal:
Proc. Amer. Math. Soc. 32 (1972), 42-44
MSC:
Primary 05.04
MathSciNet review:
0289316
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Additional Information
Abstract: We show here that the important Watson-Gordon five product combinatorial identity can, in fact, be deduced as a very simple and natural corollary to the classical Jacobi triple product identity.
- [1]
George
E. Andrews, A simple proof of Jacobi’s
triple product identity, Proc. Amer. Math.
Soc. 16 (1965),
333–334. MR 0171725
(30 #1952), http://dx.doi.org/10.1090/S0002-9939-1965-0171725-X
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O. L. Atkin and P.
Swinnerton-Dyer, Some properties of partitions, Proc. London
Math. Soc. (3) 4 (1954), 84–106. MR 0060535
(15,685d)
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W.
N. Bailey, On the simplification of some identities of the
Rogers-Ramanujan type, Proc. London Math. Soc. (3) 1
(1951), 217–221. MR 0043839
(13,327a)
- [4]
L. Carlitz, Some identities of Subbarao and Vidyasagar, Duke Math. J. (to appear).
- [5]
L. Carlitz and M. V. Subbarao, On an identity of Winquist and its generalization, Duke Math. J. (to appear).
- [6]
B.
Gordon, Some identities in combinatorial analysis, Quart. J.
Math. Oxford Ser. (2) 12 (1961), 285–290. MR 0136551
(25 #21)
- [7]
L.
J. Mordell, An identity in combinatorial analysis, Proc.
Glasgow Math. Assoc. 5 (1962), 197–200 (1962). MR 0138900
(25 #2340)
- [8]
D.
B. Sears, Two identities of Bailey, J. London Math. Soc.
27 (1952), 510–511. MR 0050067
(14,271a)
- [9]
Lucy
Joan Slater, Generalized hypergeometric functions, Cambridge
University Press, Cambridge, 1966. MR 0201688
(34 #1570)
- [10]
M.
V. Subbarao and M.
Vidyasagar, On Watson’s quintuple product
identity, Proc. Amer. Math. Soc. 26 (1970), 23–27. MR 0263770
(41 #8370), http://dx.doi.org/10.1090/S0002-9939-1970-0263770-2
- [11]
G. N. Watson, Theorems stated by Ramanujan. VII: Theorems on continued fractions, J. London Math. Soc. 4 (1929), 37-48.
- [12]
-, Ramanujan's Vermutung über Zerfallungsanzahlen, J. Reine Angew. Math. 179 (1938), 97-128.
- [1]
- G. E. Andrews, A simple proof of Jacobi's triple product identity, Proc. Amer. Math. Soc. 16 (1965), 333-334. MR 30 #1952. MR 0171725 (30:1952)
- [2]
- A. O. L. Atkin and P. Swinnerton-Dyer, Some properties of partitions, Proc. London Math. Soc. (3) 4 (1954), 84-106. MR 15, 685. MR 0060535 (15:685d)
- [3]
- W. N. Bailey, On the simplification of some identities of the Rogers-Ramanujan type, Proc. London Math. Soc. (3) 1 (1951), 217-221. MR 13, 327. MR 0043839 (13:327a)
- [4]
- L. Carlitz, Some identities of Subbarao and Vidyasagar, Duke Math. J. (to appear).
- [5]
- L. Carlitz and M. V. Subbarao, On an identity of Winquist and its generalization, Duke Math. J. (to appear).
- [6]
- B. Gordon, Some identities in combinatorial analysis, Quart. J. Math. Oxford Ser. (2) 12 (1961), 285-290. MR 25 #21. MR 0136551 (25:21)
- [7]
- L. J. Mordell, An identity in combinatorial analysis, Proc. Glasgow Math. Assoc. 5 (1962), 197-200. MR 25 #2340. MR 0138900 (25:2340)
- [8]
- D. B. Sears, Two identities of Bailey, J. London Math. Soc. 27 (1952), 510-511. MR 14, 271. MR 0050067 (14:271a)
- [9]
- L. J. Slater, Generalized hypergeometric functions, Cambridge Univ. Press, Cambridge, 1966. MR 34 #1570. MR 0201688 (34:1570)
- [10]
- M. V. Subbarao and M. Vidyasagar, On Watson's quintuple product identity, Proc. Amer. Math. Soc. 26 (1970), 23-27. MR 0263770 (41:8370)
- [11]
- G. N. Watson, Theorems stated by Ramanujan. VII: Theorems on continued fractions, J. London Math. Soc. 4 (1929), 37-48.
- [12]
- -, Ramanujan's Vermutung über Zerfallungsanzahlen, J. Reine Angew. Math. 179 (1938), 97-128.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1972-0289316-2
PII:
S 0002-9939(1972)0289316-2
Keywords:
Quintuple product identity,
Jacobi's triple product identity
Article copyright:
© Copyright 1972 American Mathematical Society
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