Related papers: The general harmonic-oscillator brackets: compact …
We present a new Fortran library to evaluate all harmonic polylogarithms up to weight four numerically for any complex argument. The algorithm is based on a reduction of harmonic polylogarithms up to weight four to a minimal set of basis…
We present a new approach for the Talmi-Moshinsky transformation representation in the harmonic oscillator basis. We utilize the SU(3) scheme for the calculation of harmonic oscillator brackets. Using this scheme we obtain the explicit…
A program to calculate the three-particle hyperspherical brackets is presented. Test results are listed and it is seen that the program is well applicable up to very high values of the hypermomentum and orbital momenta. The listed runs show…
In this paper, we obtain some formulae for harmonic sums, alternating harmonic sums and Stirling number sums by using the method of integral representations of series. As applications of these formulae, we give explicit formula of several…
Cartesian harmonic tensors are completely symmetric traceless tensors in three dimensional space constructed from the direct product of unit vectors. They are useful in generating expressions for the angular coupling of spherical harmonics…
This paper describes a method of calculating the transforms, currently obtained via Fourier and reverse Fourier transforms. The method allows calculating efficiently the transforms of a signal having an arbitrary dimension of the digital…
In this paper, we consider three families of numerical series with general terms containing the harmonic numbers, and we use simple methods from classical and complex analysis to find explicit formulas for their respective sums.
In this paper we present a straightforward systematic method for the exact and approximate calculation of integrals that appear in formulas for the period of anharmonic oscillators and other problems of interest in classical mechanics.
A generalized harmonic oscillator on noncommutative spaces is considered. Dynamical symmetries and physical equivalence of noncommutative systems with the same energy spectrum are investigated and discussed. General solutions of…
We demonstrate a fast spin-s spherical harmonic transform algorithm, which is flexible and exact for band-limited functions. In contrast to previous work, where spin transforms are computed independently, our algorithm permits the…
We present here a large collection of harmonic and quadratic harmonic sums, that can be useful in applied questions, e.g., probabilistic ones. We find closed-form formulae, that we were not able to locate in the literature.
Spherical Harmonic Gaussian type orbitals and Slater functions can be expressed using spherical coordinates or a linear combinations of the appropriate Cartesian functions. General expressions for the transformation coefficients between the…
In the study of alternative or extended theories of gravity, Dirac's Hamiltonian constraint algorithm is invaluable for enumerating the propagating modes and gauge symmetries. For gravity, this canonical approach is frequently applied as a…
The authors present SHarmonic, a new implementation of the spherical harmonics targeted for electronic-structure calculations. Their approach is to use explicit formulas for the harmonics written in terms of normalized Cartesian…
Through the present paper, the code gamgamZZ is presented, which may be used to calculate all possible observables related to the process $\gamma \gamma \to ZZ$, in either the Standard Model (SM), or the minimal sypersymmetric standard…
We present the FORTRAN-code HPOLY.f for the numerical calculation of harmonic polylogarithms up to w = 8 at an absolute accuracy of $\sim 4.9 \cdot 10^{-15}$ or better. Using algebraic and argument relations the numerical representation can…
We present a computer code that analytically evaluates the matrix elements of the microscopic nuclear Hamiltonian and unity operator between Slater determinants of displaced gaussian single particle orbits. Such matrix elements appear in…
Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their…
Recently, the butterfly approximation scheme and hierarchical approximations have been proposed for the efficient computation of integral transforms with oscillatory and with asymptotically smooth kernels. Combining both approaches, we…
We present a simple representation for analytically continued nested harmonic sums for the arbitrary complex argument. This representation can be obtained for a wide range of nested harmonic sums from a precomputed database for the pole…