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  • Proceedings of the Edinburgh Mathematical Society, Volume 54, Issue 2
  • June 2011, pp. 273-295

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

  • Gert Almkvist (a1), Duco van Straten (a2) and Wadim Zudilin (a3)
  • DOI:
  • Published online: 30 March 2011

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.

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8.F. Beukers , On Dwork's accessory parameter problem, Math. Z. 241 (2002), 425444.

12.B. H. Lian and S.-T. Yau , Differential equations from mirror symmetry, in Surveys in differential geometry: differential geometry inspired by string theory, Surveys in Differential Geometry, Volume 5, pp. 510526 (International Press, Boston, MA, 1999).

13.R. Miranda and U. Persson , On extremal rational elliptic surfaces, Math. Z. 193 (1986), 537558.

15.C. Peters and J. Stienstra , A pencil of K3-surfaces related to Apéry's recurrence for ζ(3) and Fermi surfaces for potential zero, in Arithmetic of complex manifolds, Lecture Notes in Mathematics, Volume 1399, pp. 110127 (Springer, 1989).

21.W. Zudilin , Quadratic transformations and Guillera's formulas for 1/π2, Math. Notes 81 (2007), 297301.

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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