We analyze the asymptotic rates of convergence of Chebyshev, Legendre and Jacobi polynomials. One complication is that there are many reasonable measures of optimality as enumerated here. Another is that there are at least three exceptions to the general principle that Chebyshev polynomials give the fastest rate of convergence from the larger family of Jacobi polynomials. When f (x) is singular...

Abstract A spectral‐Galerkin method based on Legendre‐Fourier approximation for fourth‐order problems in cylindrical regions is studied this paper. By the coordinate transformation, a three‐dimensional problem region transformed into sequence of decoupled with two dimensions and corresponding pole conditions are also derived. With appropriately constructed weighted Sobolev space, weak form esta...

Orthogonal Legendre moments are used in several pattern recognition and image processing applications. Translation and scale Legendre moment invariants were expressed as a combination of the approximate original Legendre moments. The shifted and scaled Legendre polynomials were expressed in terms of the original Legendre polynomials according to complicated and time-consuming algebraic relation...

Medical information digitization makes the medical information storage and extraction more convenient. Medical image information security and copyright protection is also gradually being taken seriously, and some medical image watermarking has been applied. According to the characteristics of three-dimensional medical images, this paper proposes a robust zero-watermarking algorithm for medical ...

Models of bio-mathematics are experimental systems that recreate aspects human tissue function, diseases or virus. In this research, a new operational matrix based on the Laguerre wavelets is introduced for arbitrary-order susceptible-infected-recovered (SIR) epidemic dynamical system childhood diseases. An exact mechanism Riemann–Liouville arbitrary integral operator explained where derivative...

Adrien-Marie Legendre (1752–1833) made great contributions to analysis, number theory, celestial mechanics, and practical science. His name is attached to the Legendre differential equation, Legendre polynomials, the Legendre transformation, the Legendre symbol in number theory, the Legendre conditions in calculus of variations, the Legendre relation for elliptic integrals, the Legendre duplica...