The aim of this paper is to present some recurrence relations arising from confluent hypergeometric functions. In addition, an explicit closed-form expression for a sequence associated the series in terms Bell partition polynomials proposed. Several examples are given illustrate our results.

We discuss the statistical mechanics of rotating self-gravitating systems by allowing properly for the conservation of angular momentum. We study analytically the case of slowly rotating isothermal spheres by expanding the solutions of the Boltzmann-Poisson equation in a series of Legendre polynomials, adapting the procedure introduced by Chandrasekhar (1933) for distorted polytropes. We show h...

After decades of experimental validation, Bell’s Theorem has changed the ontological status of local realism in physics. But recent theoretical and experimental results present a new challenge to Bell’s analysis. A geometricalgebraic challenge claims that Bell makes a topological mistake, while ‘weak measurement’ results challenge the Copenhagen Interpretation. We review these results and analy...

It is often believed that de Finetti’s coherence principle naturally leads, in the finite case, to the Kolmogorov’s probability theory of random phenomena, which then implies Bell’s inequality. Thus, not only a violation of Bell’s inequality looks paradoxical in the Kolmogorovian framework, but it should violate also de Finetti’s coherence principle. Firstly, we show that this is not the case: ...

In this paper, the authors give a simple review of closed-form, explicit, and recursive formulas related results for nth derivative power-exponential function xx, establish two closed-form explicit partial Bell polynomials at some specific arguments, present several new xx functions integer sequences.

In this talk presented at the TAU92 workshop, Colombus, OH, Sept. 92, we summarize results presented in more detail in a recent paper by S. Abel, M. Dittmar and the author where we gave a general proof that Bell's inequality can not be tested at a collider experiment. In particular, a measurement of correlated tau-spins at LEP does not constitute a test of local realistic theories via Bell's in...

We show that the recurrence relation deduced by Robbins and Osler et al for sum of divisors function can be solved in terms complete Bell polynomials. Besides, connection between number representations n as four triangular numbers allows obtain arecurrence where only participate values with m odd.

The problem of computing the Laplace transform composed functions has not found its way into literature because it was customarily believed that there were no suitable formula to solve it. Actually, been shown in previous work by making use Bell polynomials, efficient approximations can be found. Moreover, using an extension Bell’s polynomials bivariate functions, is also possible approximate t...

In this paper, by using the Bernoulli numbers and exponential complete Bell polynomials, we establish four general asymptotic expansions for hyperfactorial functions ∏ k=1 n k q , which have only odd power terms or even terms. We derive recurrences parameter sequences in these give some special recurrences.

Motivated by recent progress in quantum information theory, this article aims at optimizing trace polynomials, i.e., polynomials noncommuting variables and traces of their products. A novel Positivstellensatz certifying positivity subject to constraints is presented, a hierarchy semidefinite relaxations converging monotonically the optimum polynomial tracial provided. This can be seen as analog...