orthogonal family

orthogonal family

[ȯr′thäg·ən·əl′fam·lē]
(mathematics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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Let us now assume that [x.sup.(N).sub.1], ..., [x.sup.(N).sub.N] are the zeros of the polynomial [p.sub.N](x) from the orthogonal family [{[p.sub.v](x)}.sup.[infinity].sub.v=0], while [mathematical expression not reproducible] ,..., [mathematical expression not reproducible] are the zeros of the polynomial [mathematical expression not reproducible].
The choice of 3 dimensional orthogonal family is a plenty but what has been considered is
We study the Fourier transform of polynomials in an orthogonal family, taken with respect to the orthogonality measure.

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