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A continued fraction of order twelve

M. Mahadeva Naika, B. Dharmendra, K. Shivashankara (2008)

Open Mathematics

In this paper, we establish several explicit evaluations, reciprocity theorems and integral representations for a continued fraction of order twelve which are analogues to Rogers-Ramanujan’s continued fraction and Ramanujan’s cubic continued fraction.

Approximation properties of bivariate complex q -Bernstein polynomials in the case q > 1

Nazim I. Mahmudov (2012)

Czechoslovak Mathematical Journal

In the paper, we discuss convergence properties and Voronovskaja type theorem for bivariate q -Bernstein polynomials for a function analytic in the polydisc D R 1 × D R 2 = { z C : | z | < R 1 } × { z C : | z | < R 1 } for arbitrary fixed q > 1 . We give quantitative Voronovskaja type estimates for the bivariate q -Bernstein polynomials for q > 1 . In the univariate case the similar results were obtained by S. Ostrovska: q -Bernstein polynomials and their iterates. J. Approximation Theory 123 (2003), 232–255. and S. G. Gal: Approximation by Complex Bernstein and Convolution...

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