A Bailey Tree for Integrals
Teoretičeskaâ i matematičeskaâ fizika, Tome 139 (2004) no. 1, pp. 104-111 Cet article a éte moissonné depuis la source Math-Net.Ru

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We introduce the notion of integral Bailey pairs. Using the single-variable elliptic beta integral, we construct an infinite binary tree of identities for elliptic hypergeometric integrals. Two particular sequences of identities are described explicitly.
Keywords: Bailey pairs, Bailey chains, Bailey tree, beta integrals, elliptic hypergeometric integrals.
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V. P. Spiridonov. A Bailey Tree for Integrals. Teoretičeskaâ i matematičeskaâ fizika, Tome 139 (2004) no. 1, pp. 104-111. http://geodesic.mathdoc.fr/item/TMF_2004_139_1_a7/

[1] G. E. Andrews, “Bailey's transform, lemma, chains and tree”, Proc. NATO ASI Special functions-2000 (Tempe, USA, May 29–June 9, 2000), eds. J. Bustoz, M. E. H. Ismail, S. K. Suslov, Kluwer, Dordrecht, 2001, 1–22 | DOI | MR | Zbl

[2] S. O. Warnaar, “50 years of Bailey's lemma”, Algebraic Combinatorics and Applications, ed. A. Betten, Springer, Berlin, 2001, 333–347 | DOI | MR | Zbl

[3] V. P. Spiridonov, Int. Math. Res. Notices, 37 (2002), 1945–1977 | DOI | MR | Zbl

[4] G. E. Andrews, A. Berkovich, J. London Math. Soc. (2), 66 (2002), 529–549 | DOI | MR | Zbl

[5] V. P. Spiridonov, “Theta hypergeometric integrals”, Algebra i analiz, 15:6 (2003), 161–215 | MR | Zbl

[6] V. P. Spiridonov, “An elliptic beta integral”, Proc. Fifth Internat. Conf. on Difference Equations (Temuco, Chile, January 3–7, 2000), eds. S. Elaydi, J. Lopez Fenner, G. Ladas, M. Pinto, Taylor and Francis, London, 2001, 273–282 | MR

[7] G. Gasper, M. Rahman, Basic Hypergeometric Series, Encyclopedia of Mathematics and its Applications, 35, Cambridge Univ. Press, Cambridge, 1990 | MR | Zbl

[8] G. E. Andrews, Pacific J. Math., 114 (1984), 267–283 | DOI | MR | Zbl

[9] K. Garrett, M. E. H. Ismail, D. Stanton, Adv. Appl. Math., 23 (1999), 274–299 | DOI | MR | Zbl

[10] G. Anderson, Forum Math., 3 (1991), 415–417 ; R. Y. Denis, R. A. Gustafson, SIAM J. Math. Anal., 23 (1992), 552–561 ; R. A. Gustafson, SIAM J. Math. Anal., 25 (1994), 441–449 ; R. A. Gustafson, M. A. Rakha, Ann. Comb., 4 (2000), 347–373 ; J. F. van Diejen, V. P. Spiridonov, Int. Math. Res. Notices, 20 (2001), 1083–1110 | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl | DOI | MR | Zbl | Zbl

[11] G. E. Andrews, R. Askey, R. Roy, Special Functions, Encyclopedia of Mathematics and its Applications, 71, Cambridge Univ. Press, Cambridge, 1999 | MR | Zbl

[12] A. K. Agarwal, G. E. Andrews, D. M. Bressoud, J. Indian Math. Soc., 51 (1987), 57–73 | MR | Zbl