Ramanujan's ``lost notebook. I: Partial Theta-functions
From MaRDI portal
Publication:1160790
DOI10.1016/0001-8708(81)90013-XzbMath0477.33001MaRDI QIDQ1160790
Publication date: 1981
Published in: Advances in Mathematics (Search for Journal in Brave)
History of mathematics in the 20th century (01A60) Basic hypergeometric functions in one variable, ({}_rphi_s) (33D15) History of number theory (11-03) Elliptic functions and integrals (33E05) History of special functions (33-03) Partition identities; identities of Rogers-Ramanujan type (11P84)
Related Items (61)
Ramanujan's lost notebook. V: Euler's partition identity ⋮ A reciprocity theorem for certain \(q\)-series found in Ramanujan's lost notebook ⋮ Extensions of Ramanujan's reciprocity theorem and the Andrews-Askey integral ⋮ Generalizations of the Andrews-Yee identities associated with the mock theta functions \(\omega (q)\) and \(\nu (q)\) ⋮ Concave and convex compositions ⋮ Generalizations of Ramanujan's reciprocity theorem and their applications ⋮ Convergence of Padé approximants of partial theta functions and the Rogers-Szegö polynomials ⋮ The product of partial theta functions ⋮ Partition bijections, a survey ⋮ Ramanujan-type partial theta identities and conjugate Bailey pairs. II: Multisums ⋮ On partial sums of mock theta functions of order three ⋮ A basic bilateral series summation formula and its applications ⋮ Alternating permutations and symmetric functions ⋮ Ramanujan-type partial theta identities and conjugate Bailey pairs ⋮ Partial theta functions and mock modular forms as \(q\)-hypergeometric series ⋮ Bijective proofs using two-line matrix representations for partitions ⋮ Some identities associated with mock theta functions \(\omega (q)\) and \(\nu (q)\) ⋮ The leading root of the partial theta function ⋮ Error functions, Mordell integrals and an integral analogue of a partial theta function ⋮ Asymptotic behavior of partial and false theta functions arising from Jacobi forms and regularized characters ⋮ A new proof of the Askey-Wilson integral via a five-variable Ramanujan's reciprocity theorem ⋮ Rogers-Ramanujan type identities and Chebyshev polynomials of the third kind ⋮ An expectation formula with applications ⋮ Partitions associated with the Ramanujan/Watson mock theta functions \(\omega(q)\), \(\nu(q)\) and \(\phi(q)\) ⋮ Hardy-Petrovitch-Hutchinson's problem and partial theta function ⋮ Unnamed Item ⋮ Partial theta function expansions ⋮ PARTIAL INDEFINITE THETA IDENTITIES ⋮ Applications of an identity of Andrews ⋮ Unnamed Item ⋮ SUMS OF PARTIAL THETA FUNCTIONS THROUGH AN EXTENDED BAILEY TRANSFORM ⋮ COMBINATORIAL PROOFS OF CERTAIN IDENTITIES INVOLVING PARTIAL THETA FUNCTIONS ⋮ Classical partition functions and the \(U(n+1)\) Rogers-Selberg identity ⋮ On the Andrews-Warnaar identities for partial theta functions ⋮ BILATERAL BAILEY LEMMA AND FALSE THETA FUNCTIONS ⋮ A note on four-variable reciprocity theorem ⋮ A note on moment integrals and some applications ⋮ On certain Ramanujan's mock theta functions ⋮ Ramanujan's ``lost notebook and the Virasoro algebra ⋮ New proofs of Ramanujan's identities on false theta functions ⋮ Unnamed Item ⋮ The \(t\)-coefficient method to partial theta function identities and Ramanujan's \(_1 \psi_1\) summation formula ⋮ On the difference of partial theta functions ⋮ Mock and mixed mock modular forms in the lower half-plane ⋮ Asymptotics of generalized partial theta functions with a Dirichlet character ⋮ Quantum mock modular forms arising from eta-theta functions ⋮ On the reciprocity theorem of Ramanujan and its applications ⋮ A symmetric formula for hypergeometric series ⋮ A bijective proof of a false theta function identity from Ramanujan's lost notebook ⋮ An extension of the Andrews-Warnaar partial theta function identity ⋮ Six-variable generalization of Ramanujan's reciprocity theorem and its variants ⋮ ON SOME NEW MOCK THETA FUNCTIONS ⋮ The \(q\)-WZ method for infinite series ⋮ A framework for modular properties of false theta functions ⋮ Several transformation formulas for basic hypergeometric series ⋮ A Bailey type identity with applications related to integer representations ⋮ An identity of Andrews and the Askey-Wilson integral ⋮ Ramanujan's ``lost notebook. IV: Stacks and alternating parity in partitions ⋮ On the paper a 'lost' notebook of Ramanujan ⋮ On asymptotic formulas for certain $q$-series involving partial theta functions ⋮ Generalizations of Ramanujan's reciprocity formula and the Askey-Wilson integral
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A simple proof of Ramanujan's summation of the \(_1\Psi_1\)
- q-identities of Auluck, Carlitz, and Rogers
- Applications of Basic Hypergeometric Functions
- Shorter Notes: A Simple Proof of Ramanujan's 1 Ψ 1 Sum
- An Introduction to Ramanujan's "lost" Notebook
- ON BASIC HYPERGEOMETRIC SERIES, MOCK THETA FUNCTIONS, AND PARTITIONS (I)
- On the Geometry of Numbers in Elementary Number Theory
- Shorter Notes: On Ramanujan's Summation of 1 ψ 1 (a; b; z)
- On a Transformation of Bilateral Series with Applications
- Beiträge zur Theorie der Heineschen Reihen. Die 24 Integrale der hypergeometrischen q‐Differenzengleichung. Das q‐Analogon der Laplace‐Transformation
- On Lerch's Transcendant and the Basic Bilateral Hypergeometric Series 2 ψ2
- On the Transformation Theory of Basic Hypergeometric Functions
This page was built for publication: Ramanujan's ``lost notebook. I: Partial Theta-functions
