All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Page 1 Next

Displaying 1 – 20 of 36

Showing per page

Some infinite products with interesting continued fraction expansions

C. G. Pinner, A. J. Van der Poorten, N. Saradha (1993)

Journal de théorie des nombres de Bordeaux

We display several infinite products with interesting continued fraction expansions. Specifically, for various small values of k necessarily excluding k = 3 since that case cannot occur, we display infinite products in the field of formal power series whose truncations yield their every k -th convergent.

Sur la somme des quotients partiels du développement en fraction continue

D. Barbolosi, C. Faivre (2001)

Colloquium Mathematicae

Let [0;a₁(x),a₂(x),…] be the regular continued fraction expansion of an irrational x ∈ [0,1]. We prove mainly that, for α > 0, β ≥ 0 and for almost all x ∈ [0,1], l i m n → ∞ ( a ⁿ ₁ ( x ) + … + a ⁿ ₙ ( x ) ) / n l o g n = α / l o g 2 if α < 1 and β ≥ 0, l i m n → ∞ ( a ⁿ ₁ ( x ) + … + a ⁿ ₙ ( x ) ) / n l o g n = 1 / l o g 2 if α = 1 and β < 1, and, if α > 1 or α = 1 and β >1, l i m   i n f n → ∞ ( a ⁿ ₁ ( x ) + … + a ⁿ ₙ ( x ) ) / n l o g n = 1 / l o g 2 , l i m   s u p n → ∞ ( a ⁿ ₁ ( x ) + … + a ⁿ ₙ ( x ) ) / n l o g n = ∞ , where a ⁿ i ( x ) = a i ( x ) if a i ( x ) ≤ n α l o g β n and a ⁿ i ( x ) = 0 otherwise, for all i ∈ 1,…,n.

Currently displaying 1 – 20 of 36

Page 1 Next