Related papers: A Note on the Convolution of Circle Impulses
The goal of this paper is to extend the classical and multiplicative fractional derivatives. For this purpose, it is introduced the new extended modified Bessel function and also given an important relation between this new function…
In this note I provide two extensions of a particular case of the classical Poncelet theorem.
Considering the kernel of an integral operator intertwining two realizations of the group of motions of the pseudo-Euclidian space, we derive two formulas for series containing Whittaker's functions or Weber's parabolic cylinder functions.…
New applications of the formula $A |\psi\rangle = \langle A \rangle |\psi\rangle + \Delta A |\psi_{\perp} \rangle$ are discussed. Simple derivations of the Heisenberg uncertainty principle and of related inequalities are presented. In…
Analytical expressions are derived for classical trajectories in repulsive Coulomb plus multi-step attractive potentials. Thereafter the closed form expressions are obtained for classical deflection functions. The expressions are expected…
A calculation formula of volume of revolution with integration by parts of definite integral is derived based on monotone function, and extended to a general case that curved trapezoids is determined by continuous, piecewise strictly…
In this letter we show that the one-loop QCD $\beta$-function can be obtained from an index theorem on twistor space. This is achieved by recalling that the $\theta$-angle of self-dual gauge theory flows according the one-loop…
Expressions for the derivatives with respect to order of modified Bessel functions evaluated at integer orders and certain integral representations of associated Legendre functions with modulus argument greater than unity are used to…
In this note we give a recursive formula for the derivatives of isotropic positive definite functions on the Hilbert sphere. We then use it to prove a conjecture stated by Tr\"ubner and Ziegel, which says that for a positive definite…
An analysis of the zeta and gamma function is presented, using elementary functions like [] and {}, a general formula for the angle of zeta(1/2 + i*n) is found and the same for the gamma function.
In this note, we make a correction of the imaginary transformation formula of Chan and Liu's circular formula of theta functions. We also get the imaginary transformation formulaes for a type of generalized cubic theta functions.
In the paper, by virtue of the famous formula of Fa\`a di Bruno, with the aid of several identities of partial Bell polynomials, by means of a formula for derivatives of the ratio of two differentiable functions, and with availability of…
We continue our investigations of the analytic properties of nonlinear twists of L-functions developed in [4],[5] and [7]. Given an L-function of degree d, we first extend the transformation formula in [5], relating a twist with leading…
By employing contour integration the derivation of a generalized double finite series involving the Hurwitz-Lerch zeta function is used to derive closed form formulae in terms of special functions. We use this procedure to find special…
The purpose of this note is to provide an alternative proof of two transformation formulas contiguous to that of Kummer's second transformation for the confluent hypergeometric function ${}_1F_1$ using a differential equation approach.
The $\Delta \text{NO}$ method for static correlation is combined with second-order M{\o}ller-Plesset perturbation theory (MP2) and coupled-cluster singles and doubles (CCSD) to account for dynamic correlation. The MP2 and CCSD expressions…
In this note, we will consider two classical volume problems related to elliptic integrals. The first problem has a neat formula by means of elliptic integrals. We remade it with details. In the second problem, we found a messy formula. On…
The purpose of this note is to compare various approximation methods as applied to the inverse of the Bessel function of the first kind, in a given domain of the complex plane.
We study numerically the induction mechanisms generated from an array of helical motions distributed along a cylinder. Our flow is a very idealized geometry of the columnar structure that has been proposed for the convective motion inside…
In this paper we deal with Mellin convolution of generalized Gamma densities which leads to integrals of modified Bessel functions of the second kind. Such convolutions allow us to explicitly write the solutions of the time-fractional…