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Almkvist, Gert; van Straten, Duco; Zudilin, Wadim

Generalizations of Clausen’s formula and algebraic transformations of Calabi-Yau differential equations. (English) Zbl 1223.33007

Proc. Edinb. Math. Soc., II. Ser. 54, No. 2, 273-295 (2011).
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.
Reviewer: Som Prakash Goyal (Jaipur)

Cited in 38 Documents

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)

Keywords:

Calabi-Yau differential equation; generalized hypergeometric series; monodromy; algebraic transformation
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\textit{G. Almkvist} et al., Proc. Edinb. Math. Soc., II. Ser. 54, No. 2, 273--295 (2011; Zbl 1223.33007)
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Online Encyclopedia of Integer Sequences:

Apéry-like numbers Sum_{k=0..n} (C(n,k) * C(2*k,n))^2.
Apéry-like numbers Sum_{k=0..n} Sum_{l=0..n} (C(n,k)^2*C(n,l)*C(k,l)*C(k+l,n)).

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