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Let the number of random walks on a d-D hypercubic lattice starting at the origin which never land on the same lattice point twice in n steps be denoted c_d(n). The first few ...

Calculus I

The continued fraction for Apéry's constant zeta(3) is [1; 4, 1, 18, 1, 1, 1, 4, 1, ...] (OEIS A013631). The positions at which the numbers 1, 2, ... occur in the continued ...

The class of continuous functions is called the Baire class 0. For each n, the functions that can be considered as pointwise limits of sequences of functions of Baire class ...

A circular sector is a wedge obtained by taking a portion of a disk with central angle theta<pi radians (180 degrees), illustrated above as the shaded region. A sector with ...

A metric space X which is not complete has a Cauchy sequence which does not converge. The completion of X is obtained by adding the limits to the Cauchy sequences. For ...

Given a subset S subset R^n and a point x in S, the contingent cone K_S(x) at x with respect to S is defined to be the set K_S(x)={h:d_S^-(x;h)=0} where d_S^- is the upper ...

A general mathematical property obeyed by mathematical objects in which all elements are within a neighborhood of nearby points. The continuous maps between topological ...

Two quantities are said to be equal if they are, in some well-defined sense, equivalent. Equality of quantities a and b is written a=b. Equal is implemented in the Wolfram ...

A Fredholm integral equation of the first kind is an integral equation of the form f(x)=int_a^bK(x,t)phi(t)dt, (1) where K(x,t) is the kernel and phi(t) is an unknown ...