A semi-finite form of the quintuple product identity

2021 ◽  
Vol 184 ◽  
pp. 105509
Author(s):  
Jun-Ming Zhu ◽  
Zhi-Zheng Zhang
Keyword(s):  
Finite Form ◽  
Quintuple Product Identity ◽  
Product Identity

scholarly journals Finite form of the quintuple product identity

2006 ◽  
Vol 113 (1) ◽  
pp. 185-187 ◽  
Author(s):  
William Y.C. Chen ◽  
Wenchang Chu ◽  
Nancy S.S. Gu
Keyword(s):  
Finite Form ◽  
Quintuple Product Identity ◽  
Product Identity

scholarly journals A generalisation of the quintuple product identity

1988 ◽  
Vol 44 (1) ◽  
pp. 42-45 ◽  
Author(s):  
M. D. Hirschhorn
Keyword(s):  
General Identity ◽  
Quintuple Product Identity ◽  
Product Identity

AbstractThe quintuple product identity has appeared many times in the literature. Indeed, no fewer than 12 proofs have been given. We establish a more general identity from which the quintuple product identity follows in two ways.

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 A new form of the quintuple product identity and its application

Filomat ◽  
2017 ◽  
Vol 31 (7) ◽  
pp. 1869-1873
Author(s):  
Bhaskar Srivastava
Keyword(s):  
Simple Proof ◽  
Continued Fractions ◽  
Direct Application ◽  
General Identity ◽  
Quintuple Product Identity ◽  
Product Identity ◽  
New Form

We give a new form of the quintuple product identity. As a direct application of this new form a simple proof of known identities of Ramanujan and also new identities for other well known continued fractions are given. We also give and prove a general identity for (q3m; q3m)?.

Short and Easy Computer Proofs of the Rogers-Ramanujan Identities and of Identities of Similar Type

10.37236/1190 ◽  
1994 ◽  
Vol 1 (1) ◽  
Author(s):  
Peter Paule
Keyword(s):  
Short Proof ◽  
Similar Type ◽  
Quintuple Product Identity ◽  
Product Identity ◽  
Computer Proofs ◽  
Creative Telescoping ◽  
Ramanujan Identity

New short and easy computer proofs of finite versions of the Rogers-Ramanujan identities and of similar type are given. These include a very short proof of the first Rogers-Ramanujan identity that was missed by computers, and a new proof of the well-known quintuple product identity by creative telescoping.

scholarly journals Another simple proof of the quintuple product identity

2005 ◽  
Vol 2005 (15) ◽  
pp. 2511-2515 ◽  
Author(s):  
Hei-Chi Chan
Keyword(s):  
Simple Proof ◽  
Triple Product ◽  
Quintuple Product Identity ◽  
Product Identity

We give a simple proof of the well-known quintuple product identity. The strategy of our proof is similar to a proof of Jacobi (ascribed to him by Enneper) for the triple product identity.

A BIJECTIVE PROOF OF THE QUINTUPLE PRODUCT IDENTITY

2010 ◽  
Vol 06 (02) ◽  
pp. 247-256 ◽  
Author(s):  
SUN KIM
Keyword(s):  
Recurrence Relation ◽  
Triple Product ◽  
Jacobi’S Triple Product Identity ◽  
Bijective Proof ◽  
Quintuple Product Identity ◽  
Product Identity ◽  
Jacobi's Triple Product Identity

We give a bijective proof of the quintuple product identity using bijective proofs of Jacobi's triple product identity and Euler's recurrence relation.

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