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Displaying similar documents to “An Apéry-like difference equation for Catalan's constant.”

Hurwitz continued fractions with confluent hypergeometric functions

Takao Komatsu (2007)

Czechoslovak Mathematical Journal

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Many new types of Hurwitz continued fractions have been studied by the author. In this paper we show that all of these closed forms can be expressed by using confluent hypergeometric functions 0 F 1 ( ; c ; z ) . In the application we study some new Hurwitz continued fractions whose closed form can be expressed by using confluent hypergeometric functions.

On the length of the continued fraction for values of quotients of power sums

Pietro Corvaja, Umberto Zannier (2005)

Journal de Théorie des Nombres de Bordeaux

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Generalizing a result of Pourchet, we show that, if α , β are power sums over satisfying suitable necessary assumptions, the length of the continued fraction for α ( n ) / β ( n ) tends to infinity as n . This will be derived from a uniform Thue-type inequality for the rational approximations to the rational numbers α ( n ) / β ( n ) , n .