Ismail, Mourad E. H.; Zhang, Ruiming Integral and series representations of \(q\)-polynomials and functions. III: Theta, Ramanujan and \(q\)-Bessel functions. (English) Zbl 1506.33010 Anal. Appl., Singap. 20, No. 1, 1-18 (2022). Summary: In this paper, we use an identity connecting a modified \(q\)-Bessel function and a \({}_1 \phi_1\) function to give \(m\)-versions of entries in the Lost Notebook of Ramanujan. We also establish an identity which gives an \(m\)-version of a partition identity. We prove new relations and identities involving theta functions, the Ramanujan function, the Stieltjes-Wigert, \(q\)-Lommel and \(q\)-Bessel polynomials. We introduce and study \(q\)-analogues of the spherical Bessel functions.For Part I and II, see [ibid. 16, No. 2, 209–281 (2018; Zbl 1387.33022); the authors, Proc. Am. Math. Soc. 145, No. 9, 3717–3733 (2017; Zbl 1380.33010)] MSC: 33D15 Basic hypergeometric functions in one variable, \({}_r\phi_s\) 33D05 \(q\)-gamma functions, \(q\)-beta functions and integrals 33D45 Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.) 33D60 Basic hypergeometric integrals and functions defined by them Keywords:Rogers-Ramanujan identities; modified \(q\)-Bessel functions; basic confluent hypergeometric functions; \(m\)-versions; the Ramanujan function; Stieltjes-Wigert polynomials; \(q\)-Lommel polynomials; \(q\)-Bessel polynomials Citations:Zbl 1387.33022; Zbl 1380.33010 PDFBibTeX XMLCite \textit{M. E. H. Ismail} and \textit{R. Zhang}, Anal. Appl., Singap. 20, No. 1, 1--18 (2022; Zbl 1506.33010) Full Text: DOI References: [1] Akhiezer, N. I., The Classical Moment Problem and Some Related Questions in Analysis, English translation (Oliver and Boyd, Edinburgh, 1965). [2] Andrews, G. E., \(q\)-identities of Auluck, Carlitz, and Rogers, Duke Math. 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