Related papers: Polynomial splines interpolating prime series
In this paper, we explore the interrelationship between Eulerian numbers and B splines. Specifically, using B splines, we give the explicit formulas of the refined Eulerian numbers, and descents polynomials. Moreover, we prove that the…
Sums over inverse s-th powers of semiprimes and k-almost primes are transformed into sums over products of powers of ordinary prime zeta functions. Multinomial coefficients known from the cycle decomposition of permutation groups play the…
We consider the regular parts for basic functions of prime numbers with Riemann approximation accuracy.
In this article, we obtain upper bounds on the number of irreducible factors of some classes of polynomials having integer coefficients, which in particular yield some of the well known irreducibility criteria. For devising our results, we…
In the paper, the authors first inductively establish explicit formulas for derivatives of the arc sine function, then derive from these explicit formulas explicit expressions for a family of Bell polynomials related to the square function,…
When can a primitive of a given algebraic function be con-structed by iteratively solving algebraic equations and composing withthe primitives of some other given algebraic functions or their inverses? We establish some results in this…
Linear differential equations of arbitrary order with polynomial coefficients are considered. Specifically, necessary and sufficient conditions for the existence of polynomial solutions of a given degree are obtained for these equations. An…
We construct a smooth real-valued function P(n) in [0,1], defined via a triple integral with a periodic kernel, that approximates the characteristic function of prime numbers. The function is built to suppress when n is divisible by some m…
In the paper, the author presents diagonal recurrence relations for the Stirling numbers of the first kind. As by-products, the author also recovers three explicit formulas for special values of the Bell polynomials of the second kind.
Given a finite number of samples of a continuous set-valued function F, mapping an interval to compact subsets of the real line, we develop good approximations of F, which can be computed efficiently.
In this paper we evaluate sums and integrals of products of Fubini polynomials and have new explicit formulas for Fubini polynomials and numbers. As a consequence of these results new explicit formulas for p-Bernoulli numbers and…
We consider the functional inverse of the Gamma function in the complex plane, where it is multi-valued, and define a set of suitable branches by proposing a natural extension from the real case.
Diophantine approximation is the problem of approximating a real number by rational numbers. We propose a version of this in which the numerators are approximately related to the denominators by a Laurent polynomial. Our definition is…
Numerical study of the distribution of the Riemann zeros differences following the work [1] shows the significance of the function for which the prime sum expression is proposed. Computational results related to this definition explored…
By using the associated and restricted Stirling numbers of the second kind, we give some generalizations of the poly-Bernoulli numbers. We also study their arithmetical and combinatorial properties. As an application, at the end of the…
Prime number related fractal polygons and curves are derived by combining two different aspects. One is an approximation of the prime counting function build on an additive function. The other are prime number indexed basis entities taken…
We are interested in Moebius function and related topics!
In the paper, by establishing a new and explicit formula for computing the $n$-th derivative of the reciprocal of the logarithmic function, the author presents new and explicit formulas for calculating Bernoulli numbers of the second kind…
Recent work by Craig, van Ittersum, and Ono constructs explicit expressions in the partition functions of MacMahon that detect the prime numbers. Furthermore, they define generalizations, the MacMahonesque functions, and prove there are…
Two notable examples of dual functionals in approximation theory and computer-aided geometric design are the blossom and the divided difference operator. Both of these dual functionals satisfy a similar set of formulas and identities.…