### Table 1: Orthogonal polynomial basis functions Resolution Orthogonal polynomial basis function 0 1 x 1

"... In PAGE 3: ... FFT approximation using orthogonal polynomial basis We now propose FFT approximation using 2D separable orthogonal polynomial basis (Legendre polynomials). Table1 shows these orthogonal polynomial basis functions at three resolutions. Note that higher resolution includes the basis function of lower resolution (i.... ..."

### Table 1.2: Orthogonal polynomial basis functions k(x) for 1 k 7.

2005

### TABLE I Classical orthogonal polynomials: weight function and coefficients in the differential equation. The free parameters , and must all be larger than -1.

### Table 1 Recursion coe cients for orthogonal polynomials with Bessel weight function k dalpha(k) dbeta(k)

2002

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### Table 2 Recursion coe cients for orthogonal polynomials with Airy weight function k dalpha(k) dbeta(k)

2002

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### TABLE V THE MAXIMUM LIKELIHOOD COST FUNCTION OF THE PARAMETER VECTORS IN THE CASE OF THE ROBOT ARM (ORTHOGONAL POLYNOMIALS).

### Table 12 Number of nonzero entries in the matri- ces used for volume calculations on a triangle when Gram-Schmidt generated orthogonal polynomials and Dubiner apos;s warped basis are used as the basis functions.

1999

"... In PAGE 9: ... A typical term in the set resembles Pm( )(1? )mP2m+1;0 n ( ) where P ; n ( ) is the nth order Jacobi polynomial.7 Table12 sum- marizes the number of nonzero entries in the volume matrix for Gram-Schmidt and Dubiner apos;s warped basis sets. The sparsity for the Gram-Schmidt basis is bet- ter, but the high-order terms are quite complicated.... ..."

### TABLE II Discrete classical orthogonal polynomials: parameters, weight function, coefficients in the difference equation, and normalization constants. For the Krawtchouk case we have q = 1 ? p. Further, (b)n denotes the Pochhammer symbol. The parameters p (Krawtchouk) and c (Meixner) are restricted to the interval (0; 1). The parameters a (Charlier) and b (Meixner) are positive real numbers.

### Table 6. Estimates of coefficient matrices and resulting covariance functions and their eigenvalues for genetic and permanent environmental effects (KA and KR for A and R with lAi and lRi, respectively), fitting a cubic regression (k=4) on orthogonal polynomials of age transformed to logarithmic scale, and forcing covariance functions to have rank m=2a

"... In PAGE 18: ... Together with seven measurement error variances, that resulted in 23 and 21 parameters to be estimated for HEF and WOK, respectively. Estimates of coefficient matrices of covariances and resulting genetic and permanent environmental covariances functions together with estimates of fixed regression coefficients to model the population trajectory are summarized in Table6 . Corresponding estimates of measurement error variances are given in Table 7.... In PAGE 22: ... (1990), eigenvalues and eigenfunctions of genetic CFs provide an insight into the way selection affects the character under consideration. Estimates of the first two eigenvalues of A are given in Table6 and the corresponding eigenfunctions are shown in Figure 14. The third, significant eigenvalue for A in HEF was 64.... ..."