Some Integral Identities for Spherical Harmonics in an Arbitrary Dimension
نویسندگان
چکیده
Spherical harmonics in an arbitrary dimension are employed widely in quantum theory. Spherical harmonics are also called hyperspherical harmonics when the dimension is larger than 3. In this paper, we derive some integral identities involving spherical harmonics in an arbitrary dimension.
منابع مشابه
Fast Arbitrary BRDF Shading for Low-Frequency Lighting Using Spherical Harmonics
Real-time shading using general (e.g., anisotropic) BRDFs has so far been limited to a few point or directional light sources. We extend such shading to smooth, area lighting using a low-order spherical harmonic basis for the lighting environment. We represent the 4D product function of BRDF times the cosine factor (dot product of the incident lighting and surface normal vectors) as a 2D table ...
متن کاملSome Identities for Chandrasekhar Polynomials
Basic techniques of linear algebra are used to derive some identities involving the Chandrasekhar polynomials that play a vital role in the spherical-harmonics (A) solution to basic radiative-transfer problems. @ 1997 Elsevier Science Ltd. All rights reserved
متن کاملTwo-Particle Cluster Integral in the Expansion of the Dielectric Constant
We study in detail the two-particle cluster integral in the cluster expansion for the effective dielectric constant of a suspension of spherically symmetric polarizable inclusions embedded in a uniform medium. Although our form for the integrand differs from that derived earlier by Finkel'berg and by Jeffrey, we show that the integral is equivalent. The two-body dielectric problem for particles...
متن کاملCasimir effects of nano objects in fluctuating scalar and electromagnetic fields: Thermodynamic investigating
Casimir entropy is an important aspect of casimir effect and at the nanoscale is visible. In this paper, we employ the path integral method to obtain a general relation for casimir entropy and internal energy of arbitrary shaped objects in the presence of two, three and four dimension scalar fields and the electromagnetic field. For this purpose, using Lagrangian and based on a perturb...
متن کاملNonlocal Electrostatics in Spherical Geometries Using Eigenfunction Expansions of Boundary-Integral Operators.
In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical ha...
متن کامل