Utilizing the fact that solid-harmonic combinations of Cartesian and Hermite Gaussian atomic orbitals are identical, a new scheme for the evaluation of molecular integrals over solid-harmonic atomic orbitals is presented, where the integration is carried out over Hermite rather than Cartesian atomic orbitals. Since Hermite Gaussians are defined as derivatives of spherical Gaussians, the corresp...

Perceptual harmonic cepstral coefficients (PHCC) are proposed as features to extract from speech for recognition in noisy environments. A weighting function, which depends on the prominence of the harmonic structure, is applied to the power spectrum to ensure accurate representation of the voiced speech spectral envelope. The harmonics weighted power spectrum undergoes mel-scaled band-pass filt...

This article deals with a quantum-mechanical system which generalizes the ordinary isotropic harmonic oscillator system. We give the coefficients connecting the polar and Cartesian bases for D = 2 and the coefficients connecting the Cartesian and cylindrical bases as well as the cylindrical and spherical bases for D = 3. These interbasis expansion coefficients are found to be analytic continuat...

Computation of the spherical harmonic rotation coefficients or elements of Wigner’s dmatrix is important in a number of quantum mechanics and mathematical physics applications. Particularly, this is important for the Fast Multipole Methods in three dimensions for the Helmholtz, Laplace and related equations, if rotation-based decomposition of translation operators are used. In these and related...

A continuous function f u iv is a complex-valued harmonic function in a simply connected complex domain D ⊂ C if both u and v are real harmonic in D. It was shown by Clunie and Sheil-Small 1 that such harmonic function can be represented by f h g, where h and g are analytic in D. Also, a necessary and sufficient condition for f to be locally univalent and sense preserving in D is that |h′ z | >...

A wide range of nonlinear optical coefficients and various systems of notation have been used to describe optical second-harmonic generation (5MG). To avoid possible confusion, the techniques of optical nonlinear coefficient measurement and the elementary theory of SHG are briefly reviewed. Absolute and relative nonlinear coefficient measurements by phase-matched SHG are described. The followin...

In this paper we evaluate Euler-like sums involving harmonic/odd harmonic numbers and central binomial coefficients by using the expansion for powers of inverse sine function. We also a number integrals which in turn give rise to new coefficient identities.

The Earth’s gravitational field is represented by its multipole moments. Multipole moments have two kinds of equivalent forms, that is, the Cartesian symmetric and tracefree tensors and the spherical harmonic coefficients. The relation between these two forms is interesting and useful for some practical problems. Under Newtonian approximation, there exists a simple relation between the aforesai...

This paper introduces a new method for approximating the Biot-Savart integral for elliptical Gaussian functions using high-order interpolation and compares it to an existing method based on small aspect ratio asymptotics. The new evaluation technique uses polynomials to approximate the kernel corresponding to the integral representation of the streamfunction. We determine the polynomial coeffic...