Università degli studi Roma Tre
Dipartimento di Matematica e Fisica
We develop some extensions of the classical Bell polynomials, previously obtained, by introducing a further class of these polynomials called multidimensional Bell polynomials of higher order. They arise considering the derivatives of... more
The interior and exterior Robin problems for the Helmholtz equation in starlike planar domains are addressed by using a suitable Fourier-like technique. Attention is in particular focused on normal-polar domains whose boundaries are... more
By using some preceding results of Buendia et al., in: Alfaro et al. (Eds.), Orthogonal Polynomials and their Applications,
After recalling the most important properties of the Bell polynomials, we show how to approximate a positive compact operator by a suitable matrix. Then, we derive a representation formula for functions of the obtained matrix, which can... more
We first introduce a generalization of the Bernoulli polynomials, and consequently of the Bernoulli numbers, starting from suitable generating functions related to a class of Mittag-Leffler functions. Furthermore, multidimensional... more
We derive a general formula for computing the Newton sum rules of every polynomial belonging to a given polynomial set. We use the following tools: a recursive computation of the coefficients of the given polynomial in terms of the... more
The moments of the density of zeros of two new orthogonal polynomial systems, called Relativistic Hermite Polynomials {H(n N) (~)}n°°=0 (RHP) and Relativistic Laguerre Polynooo represented by means of a Cases' method and of a... more
We develop an extension of the classical Bell polynomials introducing the Laguerre-type version of this well-known mathematical tool. The Laguerre-type Bell polynomials are useful in order to compute thenth Laguerre-type derivatives of a... more
A generalization of the Bernoulli polynomials and, consequently, of the Bernoulli numbers, is defined starting from suitable generating functions. Furthermore, the differential equations of these new classes of polynomials are derived by... more
We denote by Γ(a) and Γ(a;z) the gamma and the incomplete gamma functions, respectively. In this paper we prove some monotonicity results for the gamma function and extend, to x > 0, a lower bound established by Elbert and Laforgia (2000)... more
We denote by I ν and K ν the Bessel functions of the first and third kind, respectively. Motivated by the relevance of the function w ν t t I ν−1 t /I ν t , t > 0, in many contexts of applied mathematics and, in particular, in some... more
We prove Turán-type inequalities for some special functions by using a generalization of the Schwarz inequality.
We study the problem of the asymptotic expansion of the ratio of two gamma functions Γ (x + α)/Γ (x + β) as x → +∞, α, β 0. In particular, an alternate asymptotic formula with respect to the ones known in literature is given.
We prove some monotonicity results for the incomplete gamma function,
An eigenvalue problem for a differential operator connected with the heat conduction of a non-steady flow is considered. By using an iterative method for computing the eigenvalues of second kind Fredholm operators (see [1]-[11]) we derive... more
We consider the Dirichlet problem for the Laplace equation in a starlike domain, i.e. a domain which is normal with respect to a suitable spherical coordinates system. Such a domain can be interpreted as a non-isotropically stretched unit... more