Related papers: A continued fraction expansion for a q-tangent fun…

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

We prove a continued fraction expansion for the reciprocal of a certain $q$-series. All the specialists in the world are asked whether it is new or not.

The autor propose the elementary derivation of the continued fraction expansion for function sec(x) + tan(x).

It is well known that the $(-1)$-evaluation of the enumerator polynomials of permutations (resp. derangements) by the number of excedances gives rise to tangent numbers (resp. secant numbers). Recently, two distinct $q$-analogues of the…

A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.

We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the existence of invariant measures with respect to the…

This note presents an especially short and direct variant of Hermite's proof of the simple continued fraction expansion e = [2,1,2,1,1,4,1,1,6,...] and explains some of the motivation behind it.

In this paper we define "a continued fraction expansion of the exponential integral $E_{1}(x)$ at infinity", which is analogous to the regular continued fraction expansion of real numbers, and prove that this expansion gives the same…

We use the method of generating functions to find the limit of a $q$-continued fraction, with 4 parameters, as a ratio of certain $q$-series. We then use this result to give new proofs of several known continued fraction identities,…

We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial…

In this paper we recall some results and some criteria on the convergence of matrix continued fractions. The aim of this paper is to give some properties and results of continued fractions with matrix arguments. Then we give continued…

In a recent paper G. Bhatnagar has given simple proofs of some of Ramanujan's continued fractions. In this note we show that some variants of these continued fractions are generating functions of q-Schroeder-like numbers.

In \cite{d4}, we gave a method to construct a continued fraction of the function $F(x):=e^{x}E_{1}(x)$. More precisely we define $F_{1}(x)$ as the reciprocal of $F(x)$ and we inductively define $F_{m}(x)$ as the reciprocal of ``$F_{m-1}(x)$…

In this paper we present a family of continued fraction expansions for $e^n$, with $n\ge 1$, with a simple expression having partial denominators given by arithmetic progressions. We give an estimate for the convergence speed showing that…

We prove an analog of Lagrange's Theorem for continued fractions on the Heisenberg group: points with an eventually periodic continued fraction expansion are those that satisfy a particular type of quadratic form, and vice-versa.

We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.

Recently Raayoni et al. announced various conjectures on continued fractions of fundamental constants automatically generated with machine learning techniques. In this paper we prove some of their stated conjectures for Euler number $e$ and…

We establish an equidistribution result for push-forwards of certain locally finite algebraic measures in the adelic extension of the space of lattices in the plane. As an application of our analysis we obtain new results regarding the…

It is widely believed that the continued fraction expansion of every irrational algebraic number $\alpha$ either is eventually periodic (and we know that this is the case if and only if $\alpha$ is a quadratic irrational), or it contains…

We prove an explicit formula for infinitely many convergents of Hurwitzian continued fractions that repeat several copies of the same constant and elements of one arithmetic progression, in a quasi-periodic fashion. The proof involves…