Certain q-series identities and applications to Lecture hall type partitions

1. Andrews, G.E. 1973. On the \(q\)-analog of Kummer’s theorem and applications. Duke Mathematical Journal 40: 525–528.

   Article  MathSciNet  Google Scholar 

2. Andrews, G.E., R. Askey, and R. Roy. 1999. Special functions, encyclopedia of mathematics and its applications, vol. 71. Cambridge: Cambridge University Press.

   Google Scholar 

3. Andrews, G.E., S. Corteel, and C.D. Savage. 2009. On \(q\)-series identities arising from the Lecture hall partitions. International Journal of Number Theory 5 (2): 327–337.

   Article  MathSciNet  Google Scholar 

4. Bailey, W.N. 1941. A note on certain \(q\)-identities. The Quarterly Journal of Mathematics Oxford Series 12: 173–175.

   Article  MathSciNet  Google Scholar 

5. Bousquet-Mlou, Mireille, and Kimmo Eriksson. 1997. Lecture hall partitions. Ramanujan Jounal 1 (1): 101–111.

   Article  MathSciNet  Google Scholar 

6. Corteel, S., C.D. Savage, and A.V. Sills. 2012. Lecture hall sequences, q-series, and asymmetric partition identities. In Partitions, q-series, and modular forms. Developments in mathematics, ed. K. Alladi, and F. Garvan, vol 23, 53–68. New York: Springer.

7. Daum, J.A. 1942. The basic analogue of Kummer’s theorem. Bulletin of the American Mathematical Society 48: 711–713.

   Article  MathSciNet  Google Scholar 

8. Gasper, G., and M. Rahman. 1990. Basic hypergeometric series, encyclopedia of mathematics and its applications, vol. 35. Cambridge: Cambridge University Press.

   MATH  Google Scholar 

9. Gochhayat, P., et al. 2016. Interlacing properties and bounds for zeros of \(_2\phi _1\) hypergeometric and little \(q\)-Jacobi polynomials. Ramanujan Journal 40 (1): 45–62.

   Article  MathSciNet  Google Scholar 

10. Gllnitz, H. 1967. Partitionen mit Differenzenbedingungen (German). Journal für die reine und angewandte Mathematik 225: 154–190.

    MathSciNet  Google Scholar 

11. Hahn, W. 1949. Über Orthogonalpolynome, die \(q\)-Differenzengleichungen genügen. Mathematische Nachrichten 2: 4–34.

    Article  MathSciNet  Google Scholar 

12. Harsh, H.V., et al. 2016. A study of q-contiguous function relations. Communications of the Korean Mathematical Society 31 (1): 65–94.

    Article  MathSciNet  Google Scholar 

13. Rakha, M.A., A.K. Rathie, and P. Chopra. 2011. On some new contiguous relations for the Gauss hypergeometric function with applications. Computers and Mathematics with Applications 61 (3): 620–629.

    Article  MathSciNet  Google Scholar 

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