THE QUINTUPLE PRODUCT IDENTITY
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Publication:5291342
DOI10.1142/S1793042106000401zbMath1159.33300MaRDI QIDQ5291342
Publication date: 10 May 2006
Published in: International Journal of Number Theory (Search for Journal in Brave)
historytheta functionquintuple product identityJacobi triple product identitybasic hypergeometric serieselliptic functionMacdonald identity
(q)-calculus and related topics (05A30) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) Research exposition (monographs, survey articles) pertaining to special functions (33-02)
Related Items (40)
SOME INVERSE RELATIONS AND THETA FUNCTION IDENTITIES ⋮ On Applications of Roots of Unity to Product Identities ⋮ \(q\)-binomial sums toward Euler's pentagonal number theorem ⋮ A note on semi-finite forms of the quintuple product identity ⋮ THE LEVEL 12 ANALOGUE OF RAMANUJAN’S FUNCTION ⋮ \(m\)-dissections of some infinite products and related identities ⋮ The products of three theta functions and the general cubic theta functions ⋮ On a pair of identities from Ramanujan's lost notebook ⋮ Iteration process for multiple Rogers-Ramanujan identities ⋮ Vanishing coefficients in quotients of theta functions with odd moduli ⋮ Jacobi's triple-product identity and an associated family of theta-function identities ⋮ On \(\ell \)-regular bipartitions modulo \(\ell \) ⋮ Arithmetic properties for 7-regular partition triples ⋮ Winquist's identity and Ramanujan's partition congruence \(p(11n+6)\equiv 0 \pmod {11}\) ⋮ Multiple expansion formulas over root systems ⋮ Vanishing coefficients in three families of products of theta functions. II ⋮ Ramanujan-Slater type identities related to the moduli 18 and 24 ⋮ A BIJECTIVE PROOF OF THE QUINTUPLE PRODUCT IDENTITY ⋮ A general transformation for theta series associated with the quadratic form \(x^2+ky^2\) ⋮ The \(t\)-coefficient method. III: A general series expansion for the product of theta functions with different bases and its applications. ⋮ A new form of the quintuple product identity and its application ⋮ A proof of Ewell's octuple product identity ⋮ Differential equations satisfied by Eisenstein series of level 2 ⋮ On Somos' dissection identities ⋮ GENERALIZED mth ORDER JACOBI THETA FUNCTIONS AND THE MACDONALD IDENTITIES ⋮ Truncated series from the quintuple product identity ⋮ On the reciprocity theorem of Ramanujan and its applications ⋮ Bilateral Bailey lemma and Rogers-Ramanujan identities ⋮ A generalization of Schröter's formula ⋮ A semi-finite form of the quintuple product identity ⋮ Six-variable generalization of Ramanujan's reciprocity theorem and its variants ⋮ Arithmetic properties for two restricted partitions modulo powers of 5 ⋮ A family of theta-function identities related to Jacobi's triple-product identity ⋮ Unnamed Item ⋮ Some more identities of the Rogers-Ramanujan type ⋮ A combinatorial proof of a recurrence relation for the sum of divisors function ⋮ On \(k\)-restricted overpartitions ⋮ On conjectures of Koike and Somos for modular identities for the Rogers–Ramanujan functions ⋮ Triple product identity, Quintuple product identity and Ramanujan’s differential equations for the classical Eisenstein series ⋮ Vanishing coefficients in two families of quotients of theta functions
Cites Work
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- Finite form of the quintuple product identity
- Theta function identities
- Generalisations of some theorems of Ramanujan
- A direct combinatorial proof of the Jacobi identity
- Lie algebraic approaches to classical partition identities
- Infinite-dimensional algebras, Dedekind's \(\eta\)-function, classical Möbius function and the very strange formula
- On the expansion of Ramanujan's continued fraction
- A new proof of Windquist's identity
- Uniform proofs of \(q\)-series-product identities
- Powers of Euler's product and related identities
- The quintuple product identity and shifted partition functions
- On the products of three theta functions
- A three-term theta function identity and its applications
- Two theorems of Gauss and allied identities proved arithmetically
- Affine root systems and Dedekind's \(\eta\)-function
- A note on the Jacobi theta formula
- SOME IDENTITIES IN COMBINATORIAL ANALYSIS
- An identity in combinatorial analysis
- A Combinatorial Proof of the Triple Product Identity
- Applications of Basic Hypergeometric Functions
- On the quintuple product identity
- Hirschhorn's identities
- ELLIPTIC FUNCTIONS AND THE QUINTUPLE, HIRSCHHORN AND WINQUIST PRODUCT IDENTITIES
- Errata to Volume 26; Errata to Volume 27
- An elementary proof of p(11m+6)≡0 (mod 11)
- Some identities in combinatorial analysis
- Residue theorem and theta function identities
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