6 papers
Continued Fractions of Polynomial Type: Theory and Encyclopedic Dictionary
Henri Cohen
After giving a number of properties of continued fractions of polynomial type, in particular focusing on convergence properties and Bauer-Muir-Apéry acceleration techniques, we giv…
Continued Fractions and Irrationality Measures for Chowla--Selberg Gamma Quotients
Henri Cohen, Wadim Zudilin
We give 39 rapidly convergent continued fractions for Chowla--Selberg gamma quotients, and deduce good irrationality measures for 20 of them, including for $\operatorname{CS}(-3)=(…
Polynomial Continued Fractions for Algebraic Numbers
Henri Cohen
Our main result is that any real cubic algebraic number has a continued fraction expansion with polynomial coefficients. Some generalizations are mentioned.
Variations on a theme of Apéry
Henri Cohen, Wadim Zudilin
Apéry's remarkable discovery of rapidly converging continued fractions with small coefficients for and has led to a flurry of important activity in an incredible vari…
A Database of Continued Fractions of Polynomial Type
Henri Cohen
We describe a database of 1883 continued fractions with polynomial coefficients, of which more than 1600 are new, both for interesting constants and for transcendental functions, a…
Apéry Acceleration of Continued Fractions
Henri Cohen
We explain in detail how to accelerate continued fractions (for constants as well as for functions) using the method used by R.~Apéry in his proof of the irrationality of . W…