Polynomial series versus sinc expansions for functions with corner or endpoint singularities
نویسندگان
چکیده
منابع مشابه
Asymptotic expansions of Legendre series coefficients for functions with endpoint singularities
Avram Sidi Computer Science Department, Technion – Israel Institute of Technology, Haifa 32000, Israel E-mail: [email protected]; URL: http://www.cs.technion.ac.il/~asidi/ Abstract. Let ∑∞ n=0 en[f ]Pn(x) be the Legendre expansion of a function f (x) on (−1, 1). In this work, we derive an asymptotic expansion as n → ∞ for en[f ], assuming that f ∈ C∞(−1, 1), but may have arbitrary algebra...
متن کاملAsymptotic expansions of Legendre series coefficients for functions with interior and endpoint singularities
Abstract. Let ∑∞ n=0 en[f ]Pn(x) be the Legendre expansion of a function f(x) on (−1, 1). In an earlier work [A. Sidi, Asymptot. Anal., 65 (2009), pp. 175–190], we derived asymptotic expansions as n → ∞ for en[f ], assuming that f ∈ C∞(−1, 1), but may have arbitrary algebraic-logarithmic singularities at one or both endpoints x = ±1. In the present work, we extend this study to functions f(x) t...
متن کاملEuler-Maclaurin expansions for integrals with arbitrary algebraic endpoint singularities
In this paper, we provide the Euler–Maclaurin expansions for (offset) trapezoidal rule approximations of the divergent finite-range integrals ∫ b a f(x) dx, where f ∈ C ∞(a, b) but can have arbitrary algebraic singularities at one or both endpoints. We assume that f(x) has asymptotic expansions of the general forms f(x) ∼ K (x− a)−1 + ∞ ∑ s=0 cs(x− a)s as x → a+, f(x) ∼ L (b− x)−1 + ∞ ∑ s=0 ds(...
متن کاملPolynomial series expansions for confluent and Gaussian hypergeometric functions
Based on the Hadamard product of power series, polynomial series expansions for confluent hypergeometric functions M(a, c; ·) and for Gaussian hypergeometric functions F (a, b; c; ·) are introduced and studied. It turns out that the partial sums provide an interesting alternative for the numerical evaluation of the functions M(a, c; ·) and F (a, b; c; ·), in particular, if the parameters are al...
متن کاملPolynomial Approximations of Functions with Endpoint Singularities and Product Integration Formulas
Several problems of mathematical physics lead to Fredholm integral equations of the second kind where the kernels are either weakly or strongly singular and the known terms are smooth. These equations have solutions which are smooth in the whole interval of integration except at the endpoints where they have mild singularities. In this paper we derive new pointwise and uniform polynomial approx...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational Physics
سال: 1986
ISSN: 0021-9991
DOI: 10.1016/0021-9991(86)90031-8