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Convolution series and the generalized convolution Taylor formula [PDF]

open access: yesFractional Calculus and Applied Analysis, 2022
19 ...
Yuri Luchko, Luchko Yuri
exaly   +3 more sources

An Algorithm for the Convolution of Legendre Series [PDF]

open access: yesSIAM Journal of Scientific Computing, 2014
An $\mathcal{O}(N^2)$ algorithm for the convolution of compactly supported Legendre series is described. The algorithm is derived from the convolution theorem for Legendre polynomials and the recurrence relation satisfied by spherical Bessel functions. Combining with previous work yields an $\mathcal{O}(N^2)$ algorithm for the convolution of Chebyshev ...
Nicholas Hale, Alex Townsend
exaly   +3 more sources

Some convolution series identities

open access: yesMathematical and Computer Modelling, 1995
A representation of a convolution series involving arbitrary sequences is obtained in terms of the derivatives of known generating functions. Another variation of the main result is given, and applications are shown to yield certain combinatorial identities and addition formulas.
R K Raina, H M Srivastava
exaly   +2 more sources
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A Convolution Structure for Jacobi Series

American Journal of Mathematics, 1969
Gangolli [6] discovered this convolution structure for special values of ac and J3 namely /3= 1/2, a = (n -1)/2; 3=0, ac n; and /3=1, a-2n + 1; 1 G= 3, c = 7. n here is a non-negative integer. Let P (a,0) (x) be the Jacobi polynomial of degree n, order (2,/) defined by P(?()are orthogonal onl (-1, 1) writh resplect tO ( 1 0x)at(1 ?
Askey, R., Wainger, S.
openaire   +2 more sources

Series concatenation of 2D convolutional codes

2015 IEEE 9th International Workshop on Multidimensional (nD) Systems (nDS), 2015
In this paper we study two-dimensional (2D) con-volutional codes which are obtained from series concatenation of two 2D convolutional codes. In this preliminary work we confine ourselves to dealing with finite-support 2D convolutional codes and make use of the so-called Fornasini-Marchesini input-state-output (ISO) model representations. In particular,
Joan-Josep Climent   +3 more
openaire   +2 more sources

Convolutional Neural Networks with Dynamic Convolution for Time Series Classification

2021
Due to its prominent applications, time series classification is one of the most important fields of machine learning. Although there are various approaches for time series classification, dynamic time warping (DTW) is generally considered to be a well-suited distance measure for time series.
Krisztián Búza, Margit Antal
openaire   +1 more source

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