Other machines on which the adaption has been tested: CRAY-i Other machines on which the adaption has been tested: CRAY-i and 1BM4341/2 No. of bits in a byte: 8 No. of bits in a byte: 8 No. of lines required to effect adaptation: 190 No. of lines required to effect adaptation: 215 Additional keywords: spherical oscillator functions . Additional keywords: Gauss—Legendre quadrature, isotopic subs...

The spectral method with discrete spherical harmonics transform plays an important role in many applications. In spite of its advantages, the spherical harmonics transform has a drawback of high computational complexity, which is determined by that of the associated Legendre transform, and the direct computation requires time of O(N3) for cut-off frequency N . In this paper, we propose a fast a...

The Legendre polynomial expansion method (LPEM), which has been successfully applied to homogenous and longitudinally inhomogeneous gratings [J. Opt. Soc. Am. B24, 2676 (2007)], is now generalized for the efficient analysis of arbitrary-shaped surface relief gratings. The modulated region is cut into a few sufficiently thin arbitrary-shaped subgratings of equal spatial period, where electromagn...

The usual method of separation of variables to find a basis of solutions of Laplace’s equation in toroidal coordinates is particularly appropriate for axially symmetric applications; for example, to find the potential outside a charged conducting torus. An alternative procedure is presented here that is more appropriate where the boundary conditions are independent of the spherical coordinate y...

The Müntz-Legendre polynomials arise by orthogonalizing the Müntz system {xxo, xx¡, ...} with respect to Lebesgue measure on [0, 1]. In this paper, differential and integral recurrence formulae for the Müntz-Legendre polynomials are obtained. Interlacing and lexicographical properties of their zeros are studied, and the smallest and largest zeros are universally estimated via the zeros of Lague...

In this paper, a Legendre sequence of period p for any odd prime p is explicitely represented as a sum of trace functions from G F(2n) to G F(2), where n is the order of 2 mod p.

We consider a fourth-order eigenvalue problem on a semi-infinite strip which arises in the study of viscoelastic shear flow. The eigenvalues and eigenfunctions are computed by a spectral method involving Laguerre functions and Legendre polynomials.

This note reports on the recent advancements in the search for explicit representation , in classical special functions, of the solutions of the fourth-order linear ordinary differential equations named Bessel-type, Jacobi-type, Laguerre-type, Legendre-type.

In the main theorem of this paper we show that any involution on the class of lower semi-continuous convex functions which is order-reversing, must be, up to linear terms, the well known Legendre transform.

We derive analogues of theorems of Ramanujan, Koshliakov and Guinand for primitive characters. As particular examples, transformation formulas involving the Legendre symbol and sums-of-divisors functions are established.