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Generalizations of Clausen's Formula and algebraic transformations of Calabi–Yau differential equations

Part of: Combinatorics Surfaces and higher-dimensional varieties Complex manifolds Singularities Families, fibrations

Published online by Cambridge University Press:  30 March 2011

Gert Almkvist ,
Duco van Straten  and
Wadim Zudilin
Gert Almkvist
Affiliation:
Matematikcentrum, Lunds Universitet, Matematik MNF, Box 118, 22100 Lund, Sweden ([email protected])
Duco van Straten
Affiliation:
Fachbereich Mathematik 08, Institut für Mathematik, AG Algebraische Geometrie, Johannes Gutenberg-Universität, 55099 Mainz, Germany ([email protected])
Wadim Zudilin
Affiliation:
School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan, NSW 2308, Australia ([email protected])
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Abstract

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We provide certain unusual generalizations of Clausen's and Orr's theorems for solutions of fourth-order and fifth-order generalized hypergeometric equations. As an application, we present several examples of algebraic transformations of Calabi–Yau differential equations.

Keywords

Calabi–Yau differential equationgeneralized hypergeometric seriesmonodromyalgebraic transformation

MSC classification

Secondary: 33C20: Generalized hypergeometric series, $_pF_q$ 05A10: Factorials, binomial coefficients, combinatorial functions 05A19: Combinatorial identities, bijective combinatorics 14D05: Structure of families (Picard-Lefschetz, monodromy, etc.) 14J32: Calabi-Yau manifolds 32Q25: Calabi-Yau theory 32S40: Monodromy; relations with differential equations and $D$-modules
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 54 , Issue 2 , June 2011 , pp. 273 - 295
Copyright
Copyright © Edinburgh Mathematical Society 2011

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