A unique method to evaluate the general integral $\\int_0^\\infty dx\\frac{\\sin ^a px \\cos ^c qx}{x^b} $ All integrals available in literature and books, that are related to Sinc(=sin x/x) function, are special cases of the general form of the integral given i... JA Nat...
When evaluating an integral with one boundary at infinity, {eq}\int_a^{\infty} f(x) dx = lim_{A \rightarrow \infty} \int_a^{A} f(x) dx {/eq}. If both of the boundaries of the integral are infinity, the integral must be broken up, such as...
The simple and double layer potentials for second order linear strongly elliptic differential operators on Lipschitz domains are studied and it is shown that in a certain range of Sobolev spaces, results on continuity and regularity can be obtained without using either Calderón's theorem on the $...
="BASELINE" border="0">proper-hypergeometric<img src="/content/RVQ6016XN5G3X826/xxlarge8217.gif" alt="rsquo" align="BASELINE" border="0"> multisum/integral identity, orq-identity, with a fixed number of summations and/or integration signs, possesses a short, computer-constructible proof...
A note on an inequality for the integral ∫ a b f(x)g(x)dx 来自 ResearchGate 喜欢 0 阅读量: 22 作者: X Sun 年份: 1998 收藏 引用 批量引用 报错 分享 全部来源 求助全文 ResearchGate 相似文献A note on an inequality due to Greene A simpler proof of the Gronwall type inequality ...
First, we talk about the limit of a sum as n→∞. Second, the boundaries of the region are called the limits of integration.We call the function f(x) the integrand, and the dx indicates that f(x) is a function with respect to x, called the variable of integration. Note that, ...
in which the eigenvalues λ of the integral equation: y(P) = λ∫ K(P,Q)y(Q)dQ + f(P) cannot have a limit.A class of the integral equations with no eigenvalues.#The integral equation:$\varphi ({\it x}) = \lambda \int_0^ \infty \sin({\it x} \xi)\varphi (\xi)d\xi$...
(2005) On Quadratic Integral Equation of Fractional Orders. ournal of Mathematical Analysis and Ap- plications, 311, 112-119. http://dx.doi.org/10.1016/j.jmaa.2005.02.012Darwish M. A., On quadratic integral equation of fractional orders, J. Math. Anal. Appl. 311 (2005), 112-119....
For a Gaussian process X and smooth function f, we consider a Stratonovich integral of f(X), defined as the weak limit, if it exists, of a sequence of Riemann sums. We give covariance conditions on X such that the sequence converges in law. This gives a change-of-variable formula in ...
The integrals module in SymPy implements methods to calculate definite and indefinite integrals of expressions.Principal method in this module is integrate()integrate(f, x) returns the indefinite integral \(\int f\,dx\) integrate(f, (x, a, b)) returns the definite integral \(\int_{a}^{b...