Related papers: A formula for constructing Mignotte sequences
In an earlier paper we introduced the notion of 'bifurcating continued fractions' in a heuristic manner. In this paper a formal theory is developed for the 'bifurcating continued fractions'.
Given any two sequences of complex numbers, we establish simple relations between their binomial convolution and the binomial convolution of their individual binomial transforms. We employ these relations to derive new identities involving…
In this paper we constructed new q-extension of Bernstein polynomials. Fron those q-Berstein polynomials, we give some interesting properties and we investigate some applications related this q-Bernstein polynomials.
A generalization of the classical Lipschitz summation formula is proposed. It involves new polylogarithmic rational functions constructed via the Fourier expansion of certain sequences of Bernoulli--type polynomials. Related families of…
In the paper, the authors review some explicit formulas and establish a new explicit formula for Bernoulli and Genocchi numbers in terms of Stirling numbers of the second kind.
We give a survey on the different results involving the topological structure of subsums of null sequences.
A simple solution of Witten's monopole equations is given.
Another approach to constructing an upper bound for the Riemann-Farey sum is described.
We derive weighted sums, including binomial and double binomial sums, for the generalized Fibonacci sequence $\{G_m\}$ where for $m\ge 2$, $G_m=G_{m-1}+G_{m-2}$ with initial values $G_0$ and $G_1$.
We describe the construction of the slice fibration of a given one.
We provide a recursive construction of all the semi-Heyting algebras that can be defined on a chain with $n$ elements. This construction allows us to count them easily. We also compare the formula for the number of semi-Heyting chains thus…
In this paper, We use the Fourier series expansion of real variables function, We give a formula to calculate the Dirichlet character sum, and four special examples are given.
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.
An introduction and overview of constructive reverse mathematics.
We describe two new classes of onto interpolating sequences for the Dirichlet space, in particular resolving a question of Bishop. We also give a complete description of the analogous sequences for a discrete model of the Dirichlet space.
In this note, we give an exposition of the construction of Seiberg-Witten invariants.
A way to add an extra dimension is briefly discussed.
This paper presents a reinterpretation of a second-order linear recurrence sequence as a sequence of continuants derived from the convergents to a continued fraction. As a result, we are able to derive the generating function and Binet…
We introduce an elementary argument to the theory of distribution of sequences modulo one.
This is an elementary explanation of a cubic composition formula due to Ramanujan.