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int_0^inftye^(-ax)J_0(bx)dx=1/(sqrt(a^2+b^2)), where J_0(z) is the zeroth order Bessel function of the first kind.

The second-order ordinary differential equation y^('')-[(m(m+1)+1/4-(m+1/2)cosx)/(sin^2x)+(lambda+1/2)]y=0.

A polynomial with matrix coefficients. An nth order matrix polynomial in a variable t is given by P(t)=A_0+A_1t+A_2t^2+...+A_nt^n, where A_k are p×p square matrices.

The second-order ordinary differential equation y^('')+[alpha/(cosh^2(ax))+betatanh(ax)+gamma]y=0.

An octic curve is an algebraic curve of order eight. The pear curve is an example of an octic curve.

A rooted tree in which the order of the subtrees is significant. There is a one-to-one correspondence between ordered forests with n nodes and binary trees with n nodes.

An Abelian planar difference set of order n exists only for n a prime power. Gordon (1994) has verified it to be true for n<2000000.

The coloring red of two complete subgraphs of n/2 points (for even n) in order to generate a blue-empty graph.

A method for constructing magic squares of odd order, also called de la Loubere's method.

A Skolem sequence of order n is a sequence S={s_1,s_2,...,s_(2n)} of 2n integers such that 1. For every k in {1,2,...,n}, there exist exactly two elements s_i,s_j in S such ...