In this paper, we propose a new generalization of the Poisson distribution by using concept weighted distribution; trigonometric weight with cosine function is used. We derive some distributional properties distribution, such as cumulative function, moment generating factorial moments, and index dispersion. Then, related model considered for modeling purposes, estimation parameters performed vi...

The generalized p-trigonometric and (p, q)-trigonometric functions were introduced by P. Lindqvist and S. Takeuchi, respectively. We prove some inequalities and present a few conjectures for the (p, q)-functions. 2010 Mathematics Subject Classification: 33C99, 33B99

Motivated by the substantial development of special functions, we contribute to establish some rigorous results on general series identities with bounded sequences and hypergeometric functions different arguments, which are generally applicable in nature. For application purpose, apply our e.g. Trigonometric Elliptic integrals, Dilogarithmic function, Error Incomplete gamma many other functions.

This paper proposes the statistical analysis of phase-only correlation functions between two real signals with phase-spectrum differences. For real signals, their phase-spectrum differences have oddsymmetry with respect to frequency indices. We assume phase-spectrum differences between two signals to be random variables. We next derive the expectation and variance of the POC functions consideri...

An open problem around deep networks is the apparent absence of over-fitting despite large over-parametrization which allows perfect fitting of the training data. In this paper, we explain this phenomenon when each unit evaluates a trigonometric polynomial. It is well understood in the theory of function approximation that approximation by trigonometric polynomials is a “role model” for many ot...

By a classical principle of probability theory, sufficiently thin subsequences of general sequences of random variables behave like i.i.d. sequences. This observation not only explains the remarkable properties of lacunary trigonometric series, but also provides a powerful tool in many areas of analysis, such the theory of orthogonal series and Banach space theory. In contrast to i.i.d. sequenc...

Direct diameter observations of Cepheid variables are used to calibrate the Barnes-Evans Cepheid surface brightness relation. Fifty-nine separate Cepheid diameter measurements from four different optical interferometers are used to calculate surface brightnesses as a function of magnitude and color. The linear fit to Cepheid surface brightness versus color is in excellent agreement with functio...

It is known that the trigonometric Calogero-Sutherland model is obtained by the trigonometric limit (τ → √ −1∞) of the elliptic CalogeroMoser model, where (1, τ) is a basic period of the elliptic function. We show that for all square-integrable eigenstates and eigenvalues of the Hamiltonian of the Calogero-Sutherland model, if exp(2π √ −1τ) is small enough then there exist square-integrable eig...

In this paper we obtain the conditions for L-convergence of the r-th derivatives of the cosine and sine trigonometric series. These results are extensions of corresponding Sidon’s and Telyakovskii’s theorems for trigonometric series (case: r = 0).