Erratum: A sum rule for associated Legendre polynomials with spherical triangles [J. Math. Phys. 44, 849 (2003)]

On a Conjectured Inequality for a Sum of Legendre Polynomials

∗This work was financially supported by the Austrian Science Foundation (FWF) grant SFB F013 and the Christian Doppler Research Association (CDG). S. Gerhold gratefully acknowledges a fruitful collaboration and continued support by the Austrian Federal Financing Agency and Bank Austria through CDG. M. Kauers was supported by the Austrian Science Foundation FWF under SFB F013 grant number F1305 ...

Fractional differential equations with Legendre polynomials

Compactly Supported Wavelets Derived From Legendre Polynomials: Spherical Harmonic Wavelets

A new family of wavelets is introduced, which is associated with Legendre polynomials. These wavelets, termed spherical harmonic or Legendre wavelets, possess compact support. The method for the wavelet construction is derived from the association of ordinary second order differential equations with multiresolution filters. The low-pass filter associated to Legendre multiresolution analysis is ...

Traceless Symmetric Tensor Approach to Legendre Polynomials and Spherical Harmonics

In these notes I will describe the separation of variable technique for solving Laplace’s equation, using spherical polar coordinates. The solutions will involve Legendre polynomials for cases with azimuthal symmetry, and more generally they will involve spherical harmonics. I will construct these solutions using traceless symmetric tensors, but in Lecture Notes 8 I describe how the solutions i...

Matrix product and sum rule for Macdonald polynomials

We present a new, explicit sum formula for symmetric Macdonald polynomials Pλ and show that they can be written as a trace over a product of (infinite dimensional) matrices. These matrices satisfy the Zamolodchikov– Faddeev (ZF) algebra. We construct solutions of the ZF algebra from a rank-reduced version of the Yang–Baxter algebra. As a corollary, we find that the normalization of the stationa...