相关论文: A Multidimensional Analogue of the Simpson's Formu…

Let M(f) denote the Midpoint Rule and T(f) the Trapezoidal Rule for estimating integral_a^b f(x) dx. Then Simpson's Rule = tM(f) + (1-t)T(f), where t = 2/3. We generalize Simpson's Rule to multiple integrals as follows. Let D be some…

In this article, we give a formula for the generalization of the binomial coefficient to the complex numbers as a linear combination of $\sinc$ functions. We then give a general formula to compute the integral on the real line of the…

Two approximations of the integral of a class of sinusoidal composite functions, for which an explicit form does not exist, are derived. Numerical experiments show that the proposed approximations yield an error that does not depend on the…

In this paper we established a new Simpson type conformable fractional integral equality for convex functions. Based on this identity, some results related to Simpson-like type inequalities are obtained. These results are then applied to…

In this paper, we obtain some Simpson type inequalities for functions whose second derivatives absolute value or q-th power of them are Q-class functions. Also we give applications to numerical integration.

We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained…

Simple proofs of the midpoint, trapezoidal and Simpson's rules are proved for numerical integration on a compact interval. The integrand is assumed to be twice continuously differentiable for the midpoint and trapezoidal rules, and to be…

The overlapping coefficient is a fundamental measure of similarity between probability distributions. While the case of two distributions has been extensively studied, extending this measure to multiple populations presents both analytical…

In this paper, the authors establish some new estimates for the remainder term of the midpoint, trapezoid, and Simpson formula using functions whose derivatives in absolute value at certain power are s-convex. Some applications to special…

Well known Simpson's paradox is puzzling and surprising for many, especially for the empirical researchers and users of statistics. However there is no surprise as far as mathematical details are concerned. A lot more is written about the…

The Newton-Girard Formula allows one to write any elementary symmetric polynomial as a sum of products of power sum symmetric polynomials and elementary symmetric polynomials of lesser degree. It has numerous applications. We have…

A formula for calculating Extensions of (mainly integral) Polynomial Functors is established, based upon projective resolutions. Sample computations are performed, which, in particular, exhibit a surprising non-trivial extension of Divided…

In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are quasi-convex. Some applications to special means of real…

In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are quasi-convex. Some applications to special means of real…

In this paper, we introduce a new method for calculating fractional integrals and differentials. The method involves an equation that we have obtained from infinite applied integration by parts. The equation works for special class of…

In this paper we consider the approximation of a function by its interpolating multilinear spline and the approximation of its derivatives by the derivatives of the corresponding spline. We derive formulas for the uniform approximation…

In this paper, we propose an interpolation formula for periodic functions. This formula can be regarded as an analog of the Sinc approximation, which is an interpolation formula for functions defined on the entire infinite interval.…

In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are P-functions. Some applications to special means of real…

In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are ({\alpha},m)-convex.

We calculate the Fourier transform of a spherically symmetric exponential function. Our evaluation is much simpler than the known one. We use the polar coordinates and reduce the Fourier transform to the integral of a rational function of…