Transformations between basic hypergeometric series on different bases and identities of Rogers-Ramanujan type
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Publication:1144177
DOI10.1016/0022-247X(80)90076-1zbMath0443.33004MaRDI QIDQ1144177
Publication date: 1980
Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)
Combinatorial identities, bijective combinatorics (05A19) Classical hypergeometric functions, ({}_2F_1) (33C05)
Related Items (22)
On basic Horn hypergeometric functions \(\mathrm{H}_3\) and \(\mathrm{H}_4\) ⋮ On simplifications of certain \(q\)-multisums ⋮ A bibasic hypergeometric transformation associated with combinatorial identities of the Rogers-Ramanujan type ⋮ Further bibasic hypergeometric transformations and their applications ⋮ New identities for terminating balanced \(_4\phi_3\)-series ⋮ Unnamed Item ⋮ Several \(q\)-series transformation formulas and new Hecke-Rogers type series identities ⋮ Unnamed Item ⋮ Certain transformation formulae for polybasic hypergeometric series ⋮ Askey–Wilson polynomials and a double $q$-series transformation formula with twelve parameters ⋮ Transformations of non-terminating basic hypergeometric series, their contour integrals and applications to Rogers-Ramanujan identites ⋮ q-Difference Equations and Identities of the Rogers–Ramanujan–Bailey Type ⋮ An extension of Askey-Wilson's \(q\)-beta integral and its applications ⋮ Positivity preserving transformations for 𝑞-binomial coefficients ⋮ A \(q\)-summation formula, the continuous \(q\)-Hahn polynomials and the big \(q\)-Jacobi polynomials ⋮ Identities of the Rogers-Ramanujan-Bailey type ⋮ Quadratic Transformation Formulas for Basic Hypergeometric Series ⋮ Bilateral Bailey lemma and Rogers-Ramanujan identities ⋮ Some implications of the WP-Bailey tree ⋮ Some basic hypergeometric transformations and Rogers–Ramanujan type identities ⋮ Asymptotic analysis of partition identities ⋮ \(q\)-Triplicate inverse series relations with applications to \(q\)-series
Cites Work
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- Some formulas of F. H. Jackson
- Some Transformations of Basic Hypergeometric Series and Their Applications
- On Rogers-Ramanujan Type Identities Related to the Modulus 11
- Positive Integrals of Bessel Functions
- On q-Analogues of the Watson and Whipple Summations
- Certain Summation Formulae for Basic Hypergeometric Series
- GENERALIZED BASIC HYPERGEOMETRIC SERIES WITH UNCONNECTED BASES (II)
- A Transformation of Nearly-Poised Basic Hypergeometric Series
- Identities of the Rogers-Ramanujan Type
- Some Identities in Combinatory Analysis
- A New Proof of Rogers's Transformations of Infinite Series
- On the Transformation Theory of Basic Hypergeometric Functions
- Further Identities of the Rogers-Ramanujan Type
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