Results 1 to 10 of about 32,025 (151)
Euler-Maclaurin with remainder for a simple integral polytope [PDF]
Duke Mathematical Journal, 2005 We give an Euler Maclaurin formula with remainder for the sum of the values of a smooth function on the integral points in a simple integral polytope. This formula is proved by elementary methods.
Yael Karshon +2 more
exaly +4 more sources
Darboux’s formula with integral remainder of functions with two independent variables [PDF]
Applied Mathematics and Computation, 2008 In this paper the authors generalize the following well-known G. Darboux's formula of functions with single variable. Theorem A. Suppose that \(f(x)\) is defined on an interval \(I\subset {\mathbb R}\) and \(f^{(n)}(x)\) is absolutely continuous on \(I\). Let \(P_{n}(t)\) be a polynomial of degree \(n\), the coefficient of the term \(t^{n}\) equal \(a_{
Feng Qi, Qiu-Ming Luo, Bai-Ni Guo
exaly +2 more sources
Estimates of the Remainder in Taylor's Theorem Using the Henstock-Kurzweil Integral [PDF]
Czechoslovak Mathematical Journal, 2005 When a real-valued function of one variable is approximated by its $n^{th}$ degree Taylor polynomial, the remainder is estimated using the Alexiewicz and Lebesgue $p$-norms in cases where $f^{(n)}$ or $f^{(n+1)}$ are Henstock--Kurzweil integrable. When the only assumption is that $f^{(n)}$ is Henstock--Kurzweil integrable then a modified form of the $n^
Erik Talvila
exaly +3 more sources
On Properties of Karamata Slowly Varying Functions with Remainder and Their Applications
MathematicsIn this paper, we study the asymptotic properties of slowly varying functions of one real variable in the sense of Karamata. We establish analogs of fundamental theorems on uniform convergence and integral representation for slowly varying functions with
Azam A. Imomov +2 more
doaj +3 more sources
Applied Mathematics Letters, 2009 An infinite set of arbitrary functionals \(S=\{S_i(f)\}^\infty_{i=0}\) is defined in a linear vector space with a set of basis functions \(\{\Phi_i(x)\}^\infty_{i=0}\). It can be verified that under certain conditions an analytic function \(f(x)\) can have the following expansion \[ f(x)= \sum^\infty_{i=0} S_i(f)\Phi_i(x).
Mohammad Masjed-Jamei, H M Srivastava
exaly +3 more sources
Power series remainder sequences and Padé fractions over an integral domain
Journal of Symbolic Computation, 1990 An algorithm is proposed that allows to compute Padé fractions, inverses of Hankel and Toeplitz matrices and to convert a power series expansion of a rational expression back to its original form. The complexity of the algorithm is analyzed and proves to be as effective as other known algorithms.
Stanley Cabay, Peter Kossowski
exaly +3 more sources
ADI method of credit spread option pricing based on jump-diffusion model [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2021 As the main contribution of this article, we establish an option on a credit spread under a stochastic interest rate. The intense volatilities in financial markets cause interest rates to change greatly; thus, we consider a jump term in addition to a ...
R. Mohamadinejad, A. Neisy, J. Biazar
doaj +1 more source
A theoretical summation-integral scheme involving commutation function in life insurance business
Ceylon Journal of Science, 2022 The aim of this paper is to analytically extend Euler’s summation-integral quadrature to core actuarial functions based on sound judgement of numerical analytics.
M. G. Ogungbenle
doaj +1 more source
Asymptotics of Solutions of Some Integral Equations Connected with Differential Systems with a Singularity [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. Информатика, 2020 Our studies concern some aspects of scattering theory of the singular differential systems y ′ − x −1Ay − q(x)y = ρBy, x 0 with n × n matrices A, B, q(x), x ∈ (0, ∞), where A, B are constant and ρ is a spectral parameter.
M. Yu. Ignatyev
doaj +1 more source