A possibly unknown approach to the problem of finding the common term of a power series is considered. A direct formula for evaluating this common term has been obtained. This formula provides useful expressions for direct evaluation of the number of partitions of a nonnegative integer and the partitions themselves. These expressions permit easily to work with power series, evaluate nth derivat...

Physics can be modeled by PDEs or recursively as iterated functions. A method is presented to decompose iterated functions into Bell polynomials and then into the combinatoric structure Schroeder’s Fourth Problem. Consistency with complex dynamics is shown by deriving the classification of fixed points in complex dynamics.

Abstract Numerous mathematicians have studied ‘poly’ as one of the generalizations to special polynomials, such Bernoulli, Euler, Cauchy, and Genocchi polynomials. In relation this, in this paper, we introduce degenerate poly-Bell polynomials emanating from polyexponential functions which are called when $\lambda \rightarrow 0$ ?...

In this paper, we present a unified grammatical interpretation of the numbers that satisfy kind four-term recurrence relation, including Bell triangle, coefficients modified Hermite polynomials, and Bessel polynomials. Additionally, as an application, criterion for real zeros row-generating polynomials is also presented.

We present a new derivation of the asymptotic correction for bias in the estimate of information from a finite sample. The new derivation reveals a relationship between information estimates and a sequence of polynomials with combinatorial significance, the exponential (Bell) polynomials, and helps to provide an understanding of the form and behavior of the asymptotic correction for bias.

We formulate a set of Bell's inequalities for the system of two correlated neutral kaons coming from the decay of a φ-meson, without assuming CP and CP T invariance. We show that a non-vanishing value of the phenomenological parameter ε ′ would violate such inequalities, ruling out Bell's locality.

In this letter we analyze the efficacy of the entangled output of Pati-Braunstein deletion machine [3] as a teleportation channel. We analyze the possibility of it violating the Bell’s inequality. Interestingly we find that for all values of α the state does not violate the Bell’s inequality but when used as a teleportation channel can give a fidelity higher than the classical optimum (i.e 2 3 ).