Related papers: A new method for computing number PI
We introduce the continued logarithm representation of real numbers and prove results on the occurrence and frequency of digits with respect to this representation
We propose a rather elementary method to compute a certain family of integrals on the half line, depending on the integer parameters $n\geq q\geq 1$.
This note presents the basic mathematical structure of a new integer factorization method based on systems of linear Diophantine equations.
The emergent field of probabilistic numerics has thus far lacked clear statistical principals. This paper establishes Bayesian probabilistic numerical methods as those which can be cast as solutions to certain inverse problems within the…
We analyze the convergence order of an algorithm producing the digits of an absolutely normal number. Furthermore, we introduce a stronger concept of absolute normality by allowing Pisot numbers as bases, which leads to expansions with…
New improvements to compute Mie scattering quantities are presented. They are based on a detailed analysis of the various sources of error in Mie computations and on mathematical justifications. The algorithm developed on these improvements…
I describe the current status of the theory of pi pi scattering, reviewing in particular recent work on the numerical solution of Roy equations and on the matching between these and the chiral representation. I discuss numerical results on…
In this article we furnish a new simple proof of a hard identity from the theory of cubature formulas via the method of coefficients.
In this paper, we develop a novel analytic method to prove the prime number theorem in de la Vall\'ee Poussin's form: $$ \pi(x)=\operatorname{li}(x)+\mathcal O(xe^{-c\sqrt{\log x}}) $$ Instead of performing asymptotic expansion on Chebyshev…
In this note we describe a new method of counting the number of unordered factorizations of a natural number by means of a generating function and a recurrence relation arising from it, which improves an earlier result in this direction.
The primary purpose of this article is to study the asymptotic and numerical estimates in detail for higher degree polynomials in $\pi(x)$ having a general expression of the form, \begin{align*} P(\pi(x)) - \frac{e x}{\log x} Q(\pi(x/e)) +…
We present a, hopefully, elementary mathematical treatment of the computational aspects of congruent numbers, such that an amateur could understand the problem and perform their own calculations.
Using appropriate notation systems for proofs, cut-reduction can often be rendered feasible on these notations, and explicit bounds can be given. Developing a suitable notation system for Bounded Arithmetic, and applying these bounds, all…
This review gives a survey of numerical algorithms and software to simulate quantum computers.It covers the basic concepts of quantum computation and quantum algorithms and includes a few examples that illustrate the use of simulation…
This work investigates a new approach to find closed form analytical approximate solution of linear initial value problems. Classical Bernoulli polynomials have been used to derive a finite set of orthonormal polynomials and a finite…
A new formulation for the proportion of true null hypotheses $(\pi_0)$, based on the sum of all $p$-values and the average of expected $p$-value under the false null hypotheses has been proposed in the current work. This formulation of the…
In this paper we present a special formula for transforming integrals to series. The resulting series involves binomial transforms with the Taylor coefficients of the integrand. Five applications are provided for evaluating challenging…
In this didactic note, we describe a procedure to derive successive approximations of $\pi$ using Euler Beta functions. It is an interesting exercise for undergraduate students, since it involves polynomial roots, integral calculations,…
In this paper we are concerned to find the eigenvalues and eigenvectors of a real symetric matrix by applying a new numerical method similar to Jacobi method. Our approch consists to use a new orthogonal matrix. The computation of the…
Some iterative techniques are defined to solve reversible inverse problems and a common formulation is explained. Numerical improvements are suggested and tests validate the methods.