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Let sumu_k be a series with positive terms and let f(x) be the function that results when k is replaced by x in the formula for u_k. If f is decreasing and continuous for ...

An integrating factor is a function by which an ordinary differential equation can be multiplied in order to make it integrable. For example, a linear first-order ordinary ...

Integration under the integral sign is the use of the identity int_a^bdxint_(alpha_0)^alphaf(x,alpha)dalpha=int_(alpha_0)^alphadalphaint_a^bf(x,alpha)dx (1) to compute an ...

There are at least two distinct notions of an intensity function related to the theory of point processes. In some literature, the intensity lambda of a point process N is ...

The intensity measure mu of a point process X relative to a Borel set B subset R^d is defined to be the expected number of points of X falling in B. Symbolically, ...

The interior product is a dual notion of the wedge product in an exterior algebra LambdaV, where V is a vector space. Given an orthonormal basis {e_i} of V, the forms ...

A point process N on R is said to be interval stationary if for every r=1,2,3,... and for all integers i_i,...,i_r, the joint distribution of {tau_(i_1+k),...,tau_(i_r+k)} ...

An invariant set S subset R^n is said to be a C^r (r>=1) invariant manifold if S has the structure of a C^r differentiable manifold (Wiggins 1990, p. 14). When stable and ...

The notion of an inverse is used for many types of mathematical constructions. For example, if f:T->S is a function restricted to a domain S and range T in which it is ...

Inverse function integration is an indefinite integration technique. While simple, it is an interesting application of integration by parts. If f and f^(-1) are inverses of ...