Six-variable generalization of reciprocity theorem found in Ramanujan's lost notebook

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참고문헌 (19)

1. C. Adiga, "On a Reciprocity Theorem of Ramanujan", Tamsui Oxford J. Math. Sci, 22(1), pp.9~15 (2006)
2. C. Adiga, "On a three variable reciprocity theorem", South East Asian Journal of Mathematics and Mathematical Sciences, 6(2), pp.57~61 (2008)
3. G. E. Andrews, "A simple proof of Jacobi's triple product identity", Proc. Amer. Math. Soc, 16, pp.333~334 (1965)
4. G. E. Andrews, "Ramanujan's lost notebook 1: Partail Θ-functions", Adv.in Math, 41, pp.137~172 (1981)
5. R. Askey, "The q-gamma and q-beta functions", Appl.Anal, 8, pp.125~141 (1978)
6. B. C. Berndt, "Reciprocity theorem for certain q-series found in Ramanujan's lost notebook", Ramanujan J, 13, pp.27~37 (2007)
7. S. Bhargava, "Basic Bilateral Series Summation Formula and its Applications", Integral Transforms Spec. Funct, 2, pp.165~184 (1994)
8. S. Bhargava, "Some eta function identities deducible from Ramanujan's 1 1 summation", J.Math.Anal.Appl, 176(2), pp.554~568 (1993)
9. G. Gasper, "Basic hypergeometric series, 2nd edn. Encyclopedia of Mathematics and its Applications", pp.96~ (2004), Cambridge University Press
10. F. H. Jackson, "A generalization of the function Γ(n) and xⁿ", Proc.Roy.Soc.London, 74, pp.64~72 (1904)
11. C. G. J. Jacobi, "Fundamenta Nova Theoriae Functionum Ellipticarum,Fratrum Borntr~ager Regiomonti" (1881), G. Reimer
12. S. Y. Kang, "Generalizations of Ramanujan's reciprocity theorem and their applications", Journal of the London Mathematical Society, 75(1), pp.18~34 (2007)
13. Z. G. Liu, "Some operator identities and q-series transformation formulas", Discrete math, 265, pp.119~139 (2003)
14. X. R. Ma, "Six-variable generalization of Ramanujan's receprocity theorem and it's variants", J.Math.Anal.Appl, 353, pp.320~328 (2009)
15. S. Ramanujan, "The Lost Notebook and Other Unpublished Papers" (1988), Narosa
16. H. S. Shukla, "A note on the sums of certain bilateral hypergeometric series", Math. Proc.Cambridge Philos. Soc, 55, pp.262~266 (1959)
17. D. D. Somashekara, "On the three variable reciprocity theorem and its applications", AJMAA, 9(1), pp.1~9 (2012)
18. J. Thomae, "Beitr~age zur theorie der durch die Heinesche reihe", J.Reine Angew.Math, 70, pp.258~281 (1869)
19. K. R. Vasuki, "Basic bilateral hypergeometric series summation formula and its applications", Math. Student, 68, pp.211~218 (1999)