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Apéry type recurrence relations. (Spanish. English summary) Zbl 1456.11017

Summary: In the last decade, the study of recurrence relations has obtained great relevance. The generation of rational approximants has been favored with the inclusion of recurrence relations for the study of the irrationality of certain mathematical constants, in particular Apéry’s constant. This article presents, based on the Zeilberger algorithm, two recurrence relations of the Apéry type. For the result, the denominators of the rational approximations to the Apéry constant were modified.

MSC:

11B37 Recurrences
33F10 Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.)
11J72 Irrationality; linear independence over a field
11Y40 Algebraic number theory computations
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