scholarly journals QUINTUPLE PRODUCT IDENTITY AS A SPECIAL CASE OF RAMANUJAN'S 1ψ1 SUMMATION FORMULA

2011 ◽  
Vol 04 (01) ◽  
pp. 31-34
Author(s):  
S. Bhargava ◽  
Chandrashekar Adiga ◽  
M. S. Mahadeva Naika
Keyword(s):  
Summation Formula ◽  
Triple Product ◽  
Binomial Theorem ◽  
Interesting Fact ◽  
Quintuple Product Identity ◽  
Product Identity ◽  
Jacobi Triple Product Identity ◽  
Special Case

In this note we observe an interesting fact that the well-known quintuple product identity can be regarded as a special case of the celebrated 1ψ1 summation formula of Ramanujan which is known to unify the Jacobi triple product identity and the q -binomial theorem.

scholarly journals Ramanujan's remarkable summation formula as a $2$-papameter generalization of the quintuple product identity

2002 ◽  
Vol 33 (3) ◽  
pp. 285-288
Author(s):  
S. Bhargava ◽  
Chandrashekar Adiga ◽  
M. S. Mahadeva Naika
Keyword(s):  
Summation Formula ◽  
Triple Product ◽  
Binomial Theorem ◽  
Suitable Transformation ◽  
Quintuple Product Identity ◽  
Product Identity

It is well known that `Ramanujan's remarkable summation formula' unifies and generalizes the $q$-binomial theorem and the triple product identity and has numerous applications. In this note we will demonstrate how, after a suitable transformation of the series side, it can be looked upon as a $2$-parameter generalization of the quintuple product identity also.

scholarly journals Consequences of a sextuple-product identity

1987 ◽  
Vol 10 (3) ◽  
pp. 545-549
Author(s):  
John A. Ewell
Keyword(s):  
Triple Product ◽  
Product Identity ◽  
Special Cases ◽  
Jacobi Triple Product Identity

A sextuple-product identity, which essentially results from squaring the classical Gauss-Jacobi triple-product identity, is used to derive two trigonometrical identities. Several special cases of these identities are then presented and discussed.

Euler's Pentagonal Number Theorem Implies the Jacobi Triple Product Identity

Integers ◽  
2011 ◽  
Vol 11 (6) ◽  
Author(s):  
Chuanan Wei ◽  
Dianxuan Gong
Keyword(s):  
Triple Product ◽  
Product Identity ◽  
Pentagonal Number Theorem ◽  
Jacobi Triple Product Identity ◽  
Liouville’S Theorem

AbstractBy means of Liouville's theorem, we show that Euler's pentagonal number theorem implies the Jacobi triple product identity.

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