# orthogonal series

## orthogonal series

[ȯr¦thäg·ən·əl ′sir‚ēz]
(mathematics)
An infinite series each term of which is the product of a member of an orthogonal family of functions and a coefficient; the coefficients are usually chosen so that the series converges to a desired function.
References in periodicals archive ?
The orthogonal series expansion using a vector of random variables to represent the random field is widely exploited and applied in the stochastic structural systems [14-17].
The course was on Orthogonal Series, in fact it was more linked to his monograph on Hilbert Spaces [6], published in 1956, with a Note by I.
Grigorian, On the representation of functions by orthogonal series in weighted [L.
0,1]] orthogonal series, Journal of Contemporary Mathematical Analysis, 35:4(2000), 44-64.
Although several properties and applications of orthogonal series with respect to a vector measure are known ([13, 14, 21]), the question of the almost everywhere convergence of series defined by such functions has not been studied yet.
Alexits, Convergence problems of orthogonal series.
In practice, the effectiveness of the algorithms hinges on their stability behavior and the rate at which the underlying orthogonal series expansions converge to the exponential function.
Although the orthogonal series considered in this study are primarily designed to approximate the exponential of a real variable, it is worth exploring how these series will behave if the real variable x is replaced by a complex variable z.
28] YUAN XU, Summability of Fourier orthogonal series for Jacobi weight on a ball in Rd, Trans.
29] YUAN XU, Orthogonal polynomials and summability in Fourier orthogonal series on spheres and on balls, Math.

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