On convergence of function F4(1,2;2,2;z1,z2) expansion into a branched continued fraction

A CONTINUED FRACTION EXPANSION FOR A q-TANGENT FUNCTION

We prove a continued fraction expansion for a certain q–tangent function that was conjectured by Prodinger.

On the Continued Fraction Expansion of a Class of Numbers

(a general reference is Chapter I of [9]). If ξ is irrational, then, by letting X tend to infinity, this provides infinitely many rational numbers x1/x0 with |ξ − x1/x0| ≤ x 0 . By contrast, an irrational real number ξ is said to be badly approximable if there exists a constant c1 > 0 such that |ξ − p/q| > c1q for each p/q ∈ Q or, equivalently, if ξ has bounded partial quotients in its continue...

On Almost Everywhere Strong Convergence of Multidimensional Continued Fraction Algorithms

We describe a strategy which allows one to produce computer assisted proofs of almost everywhere strong convergence of Jacobi-Perron type algorithms in arbitrary dimension. Numerical work is carried out in dimension three to illustrate our method. To the best of our knowledge this is the rst result on almost everywhere strong convergence in dimension greater than two.

A Short Proof of the Simple Continued Fraction Expansion of

One of the most interesting proofs is due to Hermite; it arose as a byproduct of his proof of the transcendence of e in [5]. (See [6] for an exposition by Olds.) The purpose of this note is to present an especially short and direct variant of Hermite’s proof and to explain some of the motivation behind it. Consider any continued fraction [a0, a1, a2, . . .]. Its ith convergent is defined to be ...

A Proof of the Continued Fraction Expansion of 1/M