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Generalized Wavelet Transform Associated with Legendre Polynomials

by C.p.pandey, M.m.dixit, Rajesh Kumar
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 108 - Number 12
Year of Publication: 2014
Authors: C.p.pandey, M.m.dixit, Rajesh Kumar
10.5120/18966-0308

C.p.pandey, M.m.dixit, Rajesh Kumar . Generalized Wavelet Transform Associated with Legendre Polynomials. International Journal of Computer Applications. 108, 12 ( December 2014), 35-40. DOI=10.5120/18966-0308

@article{ 10.5120/18966-0308,
author = { C.p.pandey, M.m.dixit, Rajesh Kumar },
title = { Generalized Wavelet Transform Associated with Legendre Polynomials },
journal = { International Journal of Computer Applications },
issue_date = { December 2014 },
volume = { 108 },
number = { 12 },
month = { December },
year = { 2014 },
issn = { 0975-8887 },
pages = { 35-40 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume108/number12/18966-0308/ },
doi = { 10.5120/18966-0308 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:42:50.063606+05:30
%A C.p.pandey
%A M.m.dixit
%A Rajesh Kumar
%T Generalized Wavelet Transform Associated with Legendre Polynomials
%J International Journal of Computer Applications
%@ 0975-8887
%V 108
%N 12
%P 35-40
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The convolution structure for the Legendre transform developed by Gegenbauer is exploited to define Legendre translation by means of which a new wavelet and wavelet transform involving Legendre Polynomials is defined. A general reconstruction formula is derived.

References
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  2. U. Depczynski, Sturm-Liouville wavelets, Applied and Computational Harmonic Analysis, 5 (1998), 216-247.
  3. G. Kaiser, A Friendly Guide to Wavelets, Birkhauser Verlag, Boston (1994).
  4. R. S. Pathak, Fourier-Jacobi wavelet transform, Vijnana Parishad Anushandhan Patrika 47 (2004), 7-15.
  5. R. S. Pathak and M. M. Dixit, Continuous and discrete Bessel Wavelet transforms, J. Computational and Applied Mathematics, 160 (2003) 241-250.
  6. E. D. Rainville, Special Functions, Macmillan Co. , New York (1963).
  7. R. L. Stens and M. Wehrens, Legendre Transform Methods and Best Algebraic Approximation, Comment. Math. Prace Mat 21(2) (1980), 351-380.
Index Terms

Computer Science
Information Sciences

Keywords

Legendre function Legendre transforms Legendre convolution Wavelet transforms.

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