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An integral graph, not to be confused with an integral embedding of a graph, is defined as a graph whose graph spectrum consists entirely of integers. The notion was first ...

The function K(alpha,t) in an integral or integral transform g(alpha)=int_a^bf(t)K(alpha,t)dt. Whittaker and Robinson (1967, p. 376) use the term nucleus for kernel.

The symbol int used to denote an integral intf(x)dx. The symbol was invented by Leibniz and chosen to be a stylized script "S" to stand for "summation."

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 ...

A general integral transform is defined by g(alpha)=int_a^bf(t)K(alpha,t)dt, where K(alpha,t) is called the integral kernel of the transform.

If A and B are commutative unit rings, and A is a subring of B, then A is called integrally closed in B if every element of B which is integral over A belongs to A; in other ...

A function of the coordinates which is constant along a trajectory in phase space. The number of degrees of freedom of a dynamical system such as the Duffing differential ...

The quantity being integrated, also called the integral kernel. For example, in intf(x)dx, f(x) is the integrand.

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 ...

The process of computing or obtaining an integral. A more archaic term for integration is quadrature.