Related papers: On Euler polynomial continued fractions
Consider the representation of a rational number in the form, associated with "centered" Euclidean algorithm. We prove a new formula for the limit distribution function for sequences of rationals with bounded sum of partial quotients.
The aim of this paper is twofold. Firstly, we investigate a finite sum involving the generalized falling factorial polynomials, in some special cases of which we express it in terms of the degenerate Stirling numbers of the second kind, the…
We define a generalization of the Eulerian polynomials and the Eulerian numbers by considering a descent statistic on segmented permutations coming from the study of 2-species exclusion processes and a change of basis in a Hopf algebra. We…
We introduce a new generalization of Euler's $\varphi$-function associated with a system of polynomials of several variables. We reprove by a short direct approach certain known related identities, and study some other special cases that do…
In this paper, we investigate some properties of several Sheffer sequences of several polynomials arising from umbral calculus. From our investigation, we can derive many interesting identities of several polynomials
We reformulate several known results about continued fractions in combinatorial terms. Among them the theorem of Conway and Coxeter and that of Series, both relating continued fractions and triangulations. More general polygon dissections…
This paper concerns extension of the classical Lagrange theorem, on the eventual periodicity of continued fraction expansions of quadratic surds, and the versions of it found in the literature in the case of complex numbers. In this…
We consider different generalizations of the Euler formula and discuss the properties of the associated trigonometric functions. The problem is analyzed from different points of view and it is shown that it can be formulated in a natural…
Proper continued fractions are generalized continued fractions with positive integer numerators $a_i$ and integer denominators with $b_i\geq a_i$. In this paper we study the strength of approximation of irrational numbers to their…
Symmetrical subdivisions in the space of Jager Pairs for continued fractions-like expansions will provide us with bounds on their difference. Results will also apply to the classical regular and backwards continued fractions expansions,…
In this work, we study a continued fractions theory for the topological completion of the field of Puiseux series. As usual, we prove that any element in the completion can be developed as a unique continued fractions, whose coefficients…
We develop a theory of $p$-adic continued fractions for a quaternion algebra $B$ over $\mathbb Q$ ramified at a rational prime $p$. Many properties holding in the commutative case can be proven also in this setting. In particular, we focus…
In this paper, we investigate the monotone property of the continued fractions $G(m,\lambda)$ as a function of $m$ and $\lambda$. In particular, we obtain new inequality for the relative continued fractions.
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…
In this paper, we will constructed p-adic twisted q-l-functions which is a part of answer of the question in [8]. Finally, we will treat many interesting properties related to twisted q-Euler numbers and polynomials.
We prove certain identities involving Euler and Bernoulli polynomials that can be treated as recurrences. We use these and also other known identities to indicate connection of Euler and Bernoulli numbers with entries of inverses of certain…
Ap\'ery's remarkable discovery of rapidly converging continued fractions with small coefficients for $\zeta(2)$ and $\zeta(3)$ has led to a flurry of important activity in an incredible variety of different directions. Our purpose is to…
Special kinds of continued fractions have been proved to converge to transcendental real numbers by means of the celebrated Subspace Theorem. In this paper we study the analogous $p$--adic problem. More specifically, we deal with Browkin…
Let $K$ be a number field. We show that, up to allowing a finite set of denominators in the partial quotients, it is possible to define algorithms for $\mathfrak P$-adic continued fractions satisfying the finiteness property on $K$ for…
The Hankel transform of an integer sequence is a much studied and much applied mathematical operation. In this note, we extend the notion in a natural way to sequences of $d$ integer sequences. We explore links to generalized continued…