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2010 | 8 | 3 | 474-487
Tytuł artykułu

Some new transformations for Bailey pairs and WP-Bailey pairs

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EN
Abstrakty
EN
We derive several new transformations relating WP-Bailey pairs. We also consider the corresponding transformations relating standard Bailey pairs, and as a consequence, derive some quite general expansions for products of theta functions which can also be expressed as certain types of Lambert series.
Twórcy
Bibliografia
  • [1] Andrews G.E., Bailey’s transform, lemma, chains and tree, Special functions 2000: current perspective and future directions (Tempe, AZ), 1–22, NATO Sci. Ser. II Math. Phys. Chem., 30, Kluwer Acad. Publ., Dordrecht, 2001
  • [2] Andrews G.E., Berkovich A, The WP-Bailey tree and its implications, J. London Math. Soc.(2), 2002, 66(3), 529–549 http://dx.doi.org/10.1112/S0024610702003617
  • [3] Andrews G.E., Berndt B.C., Ramanujans Lost Notebook, Part I, Springer, 2005
  • [4] Andrews G.E., Lewis R., Liu Z.G., An identity relating a theta function to a sum of Lambert series, Bull. London Math. Soc., 2001, 33(1), 25–31 http://dx.doi.org/10.1112/blms/33.1.25
  • [5] Berndt B.C., Ramanujans Notebooks, Part III, Springer-Verlag, New York, 1991
  • [6] Berndt B.C., Ramanujans Notebooks, Part V, Springer-Verlag, New York, 1998
  • [7] Borwein J.M., Borwein P.B., A cubic counterpart of Jacobi’s identity and the AGM, Trans. Amer. Math. Soc, 1991, 323(2), 691–701 http://dx.doi.org/10.2307/2001551
  • [8] Bressoud D., Some identities for terminating q-series, Math. Proc. Cambridge Philos. Soc, 1981, 89(2), 211–223 http://dx.doi.org/10.1017/S0305004100058114
  • [9] Gasper G., Rahman M., Basic hypergeometric series, With a foreword by Richard Askey, Encyclopedia of Mathematics and its Applications, 96, Cambridge University Press, Cambridge, 2004
  • [10] Liu Q., Ma X., On the Characteristic Equation of Well-Poised Baily Chains, Ramanujan J., 2009, 18(3), 351–370 http://dx.doi.org/10.1007/s11139-007-9060-6
  • [11] Mc Laughlin J., Sills A.V., Zimmer P., Some implications of Chu’s 10Ψ10 extension of Bailey’s 6Ψ6 summation formula, preprint
  • [12] Mc Laughlin J., Zimmer P., General WP-Bailey Chains, Ramanujan J., 2010, 22(1), 11–31 http://dx.doi.org/10.1007/s11139-010-9220-y
  • [13] Mc Laughlin J., Zimmer P., Some Implications of the WP-Bailey Tree, Adv. in Appl. Math., 2009, 43(2), 162–175 http://dx.doi.org/10.1016/j.aam.2009.02.001
  • [14] Singh U.B., A note on a transformation of Bailey, Quart. J. Math. Oxford Ser. (2), 1994, 45(177), 111–116 http://dx.doi.org/10.1093/qmath/45.1.111
  • [15] Slater L.J., A new proof of Rogers’s transformations of infinite series, Proc. London Math. Soc. (2), 1951, 53, 460–475 http://dx.doi.org/10.1112/plms/s2-53.6.460
  • [16] Spiridonov V.P., An elliptic incarnation of the Bailey chain, Int. Math. Res. Not., 2002, 37, 1945–1977 http://dx.doi.org/10.1155/S1073792802205127
  • [17] Watson G.N., The Final Problem: An Account of the Mock Theta Functions, J. London Math. Soc., 1936, 11, 55–80 http://dx.doi.org/10.1112/jlms/s1-11.1.55
  • [18] Warnaar S.O, Extensions of the well-poised and elliptic well-poised Bailey lemma, Indag. Math. (N.S.), 2003, 14, 571–588 http://dx.doi.org/10.1016/S0019-3577(03)90061-9
Typ dokumentu
Bibliografia
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bwmeta1.element.doi-10_2478_s11533-010-0022-7
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