Rajeswari, V.; Rao, K. Srinivasa Generalized basic hypergeometric functions and the \(q\)-analogues of 3-\(j\) and 6-\(j\) coefficients. (English) Zbl 0751.33004 J. Phys. A, Math. Gen. 24, No. 16, 3761-3780 (1991). The authors study the relationship between basic hypergeometric functions and Racah and Clebsch-Gordan coefficients of the quantum algebra \(U_ q(sl_ 2)\). A lot of explicit expressions for these coefficients were derived earlier. The authors give new derivations for these coefficients. It is shown how properties of Racah and Clebsch-Gordan coefficients are related to those of the basic hypergeometric functions \(_ 4\phi_ 3\) and \(_ 3\phi_ 2\). Reviewer: A.U.Klimyk (Kiev) Cited in 18 Documents MSC: 33D80 Connections of basic hypergeometric functions with quantum groups, Chevalley groups, \(p\)-adic groups, Hecke algebras, and related topics 17B37 Quantum groups (quantized enveloping algebras) and related deformations 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory Keywords:Racah coefficients; basic hypergeometric functions; Clebsch-Gordan coefficients; quantum algebra PDFBibTeX XMLCite \textit{V. Rajeswari} and \textit{K. S. Rao}, J. Phys. A, Math. Gen. 24, No. 16, 3761--3780 (1991; Zbl 0751.33004) Full Text: DOI