We present a unified approach for constructing Slepian functions — also known as prolate spheroidal wave on the sphere arbitrary tensor ranks including scalar, vectorial, and rank 2 tensorial functions, using spin-weighted spherical harmonics. For special case of cap regions, we derived commuting operators, allowing numerically stable computationally efficient construction spherical-harmonic-ba...

Sound localization is an important aspect in human hearing, with interaural time difference (ITD) and interaural level difference (ILD) as two binaural cues that complement each other in this goal. Head related transfer functions (HRTFs) can be used to estimate and analyze these cues, where an HRTF representation in the spherical harmonics domain has recently been suggested for analysis. The ai...

This paper proposes an inductive method to construct bases for spaces of spherical harmonics over the unit sphere Ω2q of Cq. The bases are shown to have many interesting properties, among them orthogonality with respect to the inner product of L(Ω2q). As a bypass, we study the inner product [f, g] = f(D)(g(z))(0) over the space P(Cq) of polynomials in the variables z, z ∈ Cq, in which f(D) is t...

Recurrence relations are derived for constructing rotation matrices between complex spherical harmonics directly as polynomials of the elements of the generating3×3 rotation matrix, bypassing the intermediary of any parameters such as Euler angles. The connection to the rotation matrices for real spherical harmonics is made explicit. The recurrence formulas furnish a simple, efficient, and nume...

A code package called UNÌC is currently under development at Argonne (Argonne National Laboratory). This new code package is focused on high fidelity solutions for nuclear reactor plant operations. The focus of this paper is the development of a spherical harmonics method used to solve the neutron transport equation. This new code, called PNFE, is just one of the components of UNÌC. PNFE is tar...

The velocity potential around two spheres moving perpendicularly to the line joining their centers is given by a series of spherical harmonics. The appropriateness of the truncation is evaluated by determining the residual normal surface velocity on the spheres. In evaluating the residual normal velocity, a recursive procedure is constructed to evaluate the spherical harmonics to reduce computa...

Jaydeep P. Bardhan and Matthew G. Knepley Dept. of Molecular Biophysics and Physiology, Rush University Medical Center, Chicago IL 60612 Computation Institute, The University of Chicago, Chicago IL 60637 Abstract We present two open-source (BSD) implementations of ellipsoidal harmonic expansions for solving problems of potential theory using separation of variables. Ellipsoidal harmonics are us...