The cumulant representation of the Fourier path integral method is examined to determine the asymptotic convergence characteristics of the imaginary-time density matrix with respect to the number of path variables N included. It is proved that when the cumulant expansion is truncated at order p, the asymptotic convergence rate of the density matrix behaves like N(-(2p+1)). The complex algebra a...

In a previous paper [vdH04], we introduced a truncated version of the classical Fast Fourier Transform. When applied to polynomial multiplication, this algorithm has the nice property of eliminating the “jumps” in the complexity at powers of two. When applied to the multiplication of multivariate polynomials or truncated multivariate power series, a non-trivial asymptotic factor was gained with...

If f f denotes the truncated Lusztig Fourier transform, we show that image by of normalized characteristic function a Coxeter element is alte...

Using theorems of Fourier factorization, a recent paper [J. Opt. Soc. Am. A 13, 1870 (1996)] has shown that the truncated Fourier series of products of discontinuous functions that were used in the differential theory of gratings during the past 30 years are not converging everywhere in TM polarization. They turn out to be converging everywhere only at the limit of infinitely low modulated grat...

for some fixed τ , which is called the period of f . Though function approximation using orthogonal polynomials is very convenient, there is only one kind of periodic polynomial, that is, a constant. So, polynomials are not good for approximating periodic functions. In this case, trigonometric functions are quite useful. A large class of important computational problems falls under the category...

Here are some facts about Fourier Series — useful for pde and elsewhere. Proofs of Lemmas are easy exercises, and not given. On the other hand, proofs of LEMMAS are harder; their proofs are indicated, or a reference is given.

Let $$n\ge 3$$ be an integer and p a prime with $$p\equiv 1\pmod {n}$$ . In this paper, we show that $$\begin{aligned} {}_nF_{n-1}\bigg [\begin{array}{llll} \frac{n-1}{n}&{}\frac{n-1}{n}&{}\ldots &{}\frac{n-1}{n}\\ &{}1&{}\ldots &{}1\end{array}\bigg | \, 1\bigg ]_{p-1}\equiv -\Gamma _p\bigg (\frac{1}{n}\bigg )^n\pmod {p^3}, \end{aligned}$$ where the truncated hypergeometric series x_1&{}x_2&{}\...

an infinitely long hollow cylinder containing isotropic linear elastic material is considered under the effect of arbitrary boundary stress and thermal condition. the two-dimensional coupled thermoelastodynamic pdes are specified based on equations of motion and energy equation, which are uncoupled using nowacki potential functions. the laplace integral transform and bessel-fourier series are u...

A trigonometric curve is a real plane curve where each coordinate is given parametri-cally by a truncated Fourier series. The trigonometric curves frequently arise in various areas of mathematics, physics, and engineering. Some trigonometric curves can be also represented implicitly by bivariate polynomial equations. In this paper, we give algorithms for (a) simplifying a given parametric repre...