Some infinite product identities
Authors:
Richard Blecksmith, John Brillhart and Irving Gerst
Journal:
Math. Comp. 51 (1988), 301314
MSC:
Primary 05A17; Secondary 05A19, 11P57
MathSciNet review:
942157
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Abstract: In this paper we derive the power series expansions of four infinite products of the form where the index sets and are specified with respect to a modulus (Theorems 1, 3, and 4). We also establish a useful formula for expanding the product of two Jacobi triple products (Theorem 2). Finally, we give nonexistence results for identities of two forms.
 [1]
R. Blecksmith, The Determination of Ramanujan Pairs, Ph.D. Dissertation, University of Arizona, 1983.
 [2]
Richard
Blecksmith, John
Brillhart, and Irving
Gerst, A computerassisted investigation of
Ramanujan pairs, Math. Comp.
46 (1986), no. 174, 731–749. MR 829643
(87j:11111), http://dx.doi.org/10.1090/S00255718198608296439
 [3]
Richard
Blecksmith, John
Brillhart, and Irving
Gerst, Parity results for certain partition
functions and identities similar to theta function identities, Math. Comp. 48 (1987), no. 177, 29–38. MR 866096
(87k:11113), http://dx.doi.org/10.1090/S0025571819870866096X
 [4]
Richard
Blecksmith, John
Brillhart, and Irving
Gerst, Some infinite product
identities, Math. Comp. 51
(1988), no. 183, 301–314. MR 942157
(89f:05017), http://dx.doi.org/10.1090/S00255718198809421572
 [5]
L.
Carlitz and M.
V. Subbarao, A simple proof of the quintuple
product identity, Proc. Amer. Math. Soc. 32 (1972), 42–44. MR 0289316
(44 #6507), http://dx.doi.org/10.1090/S00029939197202893162
 [6]
John
A. Ewell, Completion of a Gaussian
derivation, Proc. Amer. Math. Soc.
84 (1982), no. 2,
311–314. MR
637190 (83a:10084), http://dx.doi.org/10.1090/S00029939198206371900
 [7]
John
A. Ewell, Some combinatorial identities and arithmetical
applications, Rocky Mountain J. Math. 15 (1985),
no. 2, 365–370. Number theory (Winnipeg, Man., 1983). MR 823248
(87h:05029), http://dx.doi.org/10.1216/RMJ1985152365
 [8]
G. H. Hardy & E. M. Wright, An Introduction to the Theory of Numbers, 4th ed., Oxford Univ. Press, Oxford, 1965.
 [1]
 R. Blecksmith, The Determination of Ramanujan Pairs, Ph.D. Dissertation, University of Arizona, 1983.
 [2]
 R. Blecksmith, J. Brillhart & I. Gerst, "A computerassisted investigation of Ramanujan pairs," Math. Comp., v. 46, 1986, pp. 731749. MR 829643 (87j:11111)
 [3]
 R. Blecksmith, J. Brillhart & I Gerst, "Parity results for certain partition functions and identities similar to theta function identities," Math. Comp., v. 48, 1987, pp. 2938. MR 866096 (87k:11113)
 [4]
 R. Blecksmith, J. Brillhart & I. Gerst, "Some infinite product identities," Abstracts Amer. Math. Soc., v. 8, 1987, p. 439. MR 942157 (89f:05017)
 [5]
 L. Carlitz & M. V. Subbarao, "A simple proof of the quintuple product identity," Proc. Amer. Math. Soc., v. 32, 1972, pp. 4244. MR 0289316 (44:6507)
 [6]
 J. A. Ewell, "Completion of a Gaussian derivation," Proc. Amer. Math. Soc., v. 84, 1982, pp. 311314. MR 637190 (83a:10084)
 [7]
 J. A. Ewell, "Some combinatorial identities and arithmetic applications," Rocky Mountain J. Math., v. 15, 1985, pp. 365370. MR 823248 (87h:05029)
 [8]
 G. H. Hardy & E. M. Wright, An Introduction to the Theory of Numbers, 4th ed., Oxford Univ. Press, Oxford, 1965.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198809421572
PII:
S 00255718(1988)09421572
Keywords:
Jacobi triple product,
quintuple product,
infinite product expansions
Article copyright:
© Copyright 1988
American Mathematical Society
