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arXiv · 1403.0483

A hypergeometric basis for the Alpert multiresolution analysis

Jeffrey S. Geronimo·Plamen Iliev
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Abstract

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.

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BibTeXRIS

Jeffrey S. Geronimo, Plamen Iliev. 2014-03-03. A hypergeometric basis for the Alpert multiresolution analysis. https://doi.org/10.1137/140963923

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