%0 Journal Article
%T A hypergeometric basis for the Alpert multiresolution analysis
%A Jeffrey S. Geronimo
%A Plamen Iliev
%J Mathematics
%D 2014
%I arXiv
%R 10.1137/140963923
%X We construct an explicit orthonormal basis of piecewise ${}_{i+1}F_{i}$ hypergeometric polynomials for the Alpert multiresolution analysis. The Fourier transform of each basis function is written in terms of ${}_2F_3$ hypergeometric functions. Moreover, the entries in the matrix equation connecting the wavelets with the scaling functions are shown to be balanced ${}_4 F_3$ hypergeometric functions evaluated at $1$, which allows to compute them recursively via three-term recurrence relations. The above results lead to a variety of new interesting identities and orthogonality relations reminiscent to classical identities of higher-order hypergeometric functions and orthogonality relations of Wigner $6j$-symbols.
%U http://arxiv.org/abs/1403.0483v2