IntegralsApplication of IntegralsDifferential EquationsVector AlgebraThree Dimensional GeometryLinear ProgrammingProbability KEA Biology Syllabus: Topics The living world Animal Kingdom Biological classification
This paper deals with Euler-type integrals and the closely related Lauricella function F-D((N)), which is a hypergeometric function of many complex variables z(1),...,z(N). For F-D((N)) new analytic continuation formulas are found that represent it in the form of Horn hypergeometric ...
[], Lemma . (see also [], Theorem .) established l'Hôpital's monotone rule that can be applied to a wide class of quotients of functions. Theorem . ([]) Let –∞ < a < b < ∞, f , g : [a, b] → R be continuous on [a, b] and...
High dimensional integrals are abundant in many fields of research including quantum physics. The aim of this paper is to develop efficient recursive strategies to tackle a class of high dimensional integrals having a special product structure with low order couplings, motivated by models in lattice ...
Fractional calculus is a pure theoretical knowledge, which has been studied and applied for many years, mainly including the calculation methods of arbitrary derivatives and fine integrals [1]. Fuzzy fractional-order ordinary differential equations are calculus equations that combine fuzzy characteristics ...
Theorem ofThis will include the Fundamental CalculusTheorem of Calculus and the definite微积分基本定理integral as an area and as a limit of asum as well as the fundamental theorem.The integral from a to x of f(t)d(t)dt/dx = f(x)Indefinite Integrals and the Net Change Theorem The ...
1. Introduction In many boundary value problems of function theory the boundary conditions contain not only the sought function, but also its derivatives up to certain order. Therefore it is useful to have formulas giving an 218 GeneralizationofI.Vekua’sintegralrepresentations integral representation ...
Namely, the Boolean truth value of the atomic formulas u ∈ v and u = v for u and v in V ( F ) is defined by transfinite recursion as follows: 〚 u ∈ v 〛 = ⋁ t ∈ dom ( v ) v ( t ) ∧ 〚 t = u 〛 , 〚 u = v 〛 = ⋀ t ∈ dom ( u ) u ...
The image moment of order (𝑝,𝑞)(p,q) is expressed by integrals (sums) on the characteristic function of 𝐷𝑘Dk multiplied by weights represented by the power functions 𝑥𝑝𝑦𝑞xpyq (𝑝,𝑞=1,2,…p,q=1,2,…). The set of moments is theoretically infinite, but it ...
[0136] The notation in Equation (13) can be simplified by Equation (14) since these integrals are not solvable in a closed form and their solutions are usually found only in tabular form. 10 F ( x ) = P ( x - m σ ) ( 14 ) ...