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Smooth Wavelet Approximations of Truncated Legendre Polynomials via the Jacobi Theta Function
Joint Authors
Spurr, M. J.
Pravica, D. W.
Randriampiry, N.
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-24, 24 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-10-16
Country of Publication
Egypt
No. of Pages
24
Main Subjects
Abstract EN
The family of nth order q-Legendre polynomials are introduced.
They are shown to be obtainable from the Jacobi theta function and to satisfy recursion relations and multiplicatively advanced differential equations (MADEs) that are analogues of the recursion relations and ODEs satisfied by the nth degree Legendre polynomials.
The nth order q-Legendre polynomials are shown to have vanishing kth moments for 0≤k Convergence results are obtained, approximations are given, a reciprocal symmetry is shown, and nearly orthonormal frames are constructed. Conditions are given under which a MADE remains a MADE under inverse Fourier transform. This is used to construct new wavelets as solutions of MADEs.
American Psychological Association (APA)
Pravica, D. W.& Randriampiry, N.& Spurr, M. J.. 2014. Smooth Wavelet Approximations of Truncated Legendre Polynomials via the Jacobi Theta Function. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-24.
https://search.emarefa.net/detail/BIM-1014993
Modern Language Association (MLA)
Pravica, D. W.…[et al.]. Smooth Wavelet Approximations of Truncated Legendre Polynomials via the Jacobi Theta Function. Abstract and Applied Analysis No. 2014 (2014), pp.1-24.
https://search.emarefa.net/detail/BIM-1014993
American Medical Association (AMA)
Pravica, D. W.& Randriampiry, N.& Spurr, M. J.. Smooth Wavelet Approximations of Truncated Legendre Polynomials via the Jacobi Theta Function. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-24.
https://search.emarefa.net/detail/BIM-1014993
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1014993