A HYPERGEOMETRIC BASIS FOR THE ALPERT MULTIRESOLUTION ANALYSIS

作者：Geronimo Jeffrey S^*; Iliev Plamen

来源：SIAM Journal on Mathematical Analysis, 2015, 47(1): 654-668.

DOI：10.1137/140963923

• multiwavelets
• hypergeometric functions
• orthogonal polynomials

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 F-2(3) hypergeometric functions. Moreover, the entries in the matrix equation connecting the wavelets with the scaling functions are shown to be balanced F-4(3) hypergeometric functions evaluated at 1, which allows us to compute them recursively via three-term recurrence relations. The above results lead to a variety of new interesting identities and orthogonality relations reminiscent of classical identities of higher-order hypergeometric functions and orthogonality relations of Wigner 6j-symbols.

• 出版日期2015