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Legendre wavelets is Formula 1, in which m, the order of Legendre polynomial and t, the time, are defined in the interval [0, 1) to satisfy Formula 2.
and obtains an expansion of the appropriate Legendre polynomial [P.
Although the order parameter is connected to the eigenvalues of the order parameter tensor (second-order alignment tensor), one can calculate it as the average of the second Legendre polynomial [P.
n](x) is the generalization of Legendre polynomial and is defined as
Noting that the Walter-Shen-Soleski method does not yield stable and accurate numerical estimates of the PSWF samples for large values of the time-bandwidth product, Karoui and Moumni [13] proposed an alternative method for computing the PSWF samples based on the Legendre polynomial expansion on [-1, 1].
The main reason for this was that preliminary comparative analysis involving several different TD models have shown that for the data and population in question a RRMs with second order Legendre polynomial for permanent environmental and additive genetic effects were found to be the best by most model selection criteria.
d] is the Legendre polynomial of degree d on [0,1], which is orthogonal to all polynomials of lower degree in [L.
The coefficients of the L4 curve was calculated from the normalized Legendre polynomial (Kirkpatric et al.
ij]) is the m-th Legendre polynomial of age, [[alpha].
HOLSHEVNIKOV, Estimation of a remainder of a Legendre polynomial generating function expansion (generalization and refinement of the Bernstein inequality, Vestnik Leningrad.
On the zeros of the integrated Legendre polynomial (4.