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Generalizations of Clausen’s formula and algebraic transformations of Calabi-Yau differential equations. (English) Zbl 1223.33007
The aim of this paper is to provide certain unusual generalizations of Clausen’s and Orr’s theorems for solutions of fourth- and fifth-order generalized hypergeometric equations. Several examples of algebraic transformations of Calabi-Yau differential equation are presented as an application of main results.

##### MSC:
 33C20 Generalized hypergeometric series, $${}_pF_q$$ 34M35 Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms 05A10 Factorials, binomial coefficients, combinatorial functions 05A19 Combinatorial identities, bijective combinatorics 14D05 Structure of families (Picard-Lefschetz, monodromy, etc.) 14J32 Calabi-Yau manifolds (algebro-geometric aspects) 32Q25 Calabi-Yau theory (complex-analytic aspects) 32S40 Monodromy; relations with differential equations and $$D$$-modules (complex-analytic aspects)
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##### References:
 [1] DOI: 10.1134/S0001434607030030 · Zbl 1144.33002 [2] Golyshev, London Mathematical Society Lecture Note Series 338 pp 88– (2007) [3] Bogner (2008) [4] DOI: 10.1007/s00209-002-0424-8 · Zbl 1023.34081 [5] Beukers, Progress in Mathematics 31 pp 47– (1983) [6] Beauville, C. R. Acad. Sci. Paris Sér. I 294 pp 657– (1982) [7] Apéry, Astérisque 61 pp 11– (1979) [8] André, Aspects of Mathematics 13 (1989) [9] Almkvist, AMS/IP Studies in Advanced Mathematics 38 pp 481– (2006) [10] Whittaker, A course of modern analysis (1927) [11] van Enckevort, AMS/IP Studies in Advanced Mathematics 38 pp 539– (2006) [12] Slater, Generalized hypergeometric functions (1966) · Zbl 0135.28101 [13] Schmickler-Hirzebruch, Schriftenreihe des Mathematischen Instituts der Universität Münster (1985) [14] Peters, Lecture Notes in Mathematics 1399 pp 110– (1989) [15] Peters, Annales Sci. École Norm. Sup. (4) 19 pp 583– (1986) [16] DOI: 10.1007/BF01160474 · Zbl 0652.14003 [17] Lian, Surveys in Differential Geometry 5 pp 510– (1999) [18] Krattenthaler, Séminaires et Congrès [19] Zagier, CRM Proceedings and Lecture Notes 47 pp 349– (2009)
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