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The Legendre polynomials, sometimes called Legendre functions of the first kind, Legendre coefficients, or zonal harmonics (Whittaker and Watson 1990, p. 302), are solutions ...

The Weierstrass elliptic functions (or Weierstrass P-functions, voiced "p-functions") are elliptic functions which, unlike the Jacobi elliptic functions, have a second-order ...

The determination of the number of alternating permutations having elements {1,2,...,n}.

A subset tau in S_n of a permutation {1,...,n} is said to contain alpha in S_k if there exist 1<=i_1<...<i_k<=n such that tau=(tau_i,...,tau_k) is order isomorphic to ...

A domatic partition is a partition of the vertices of a graph into disjoint dominating sets. The maximum number of disjoint dominating sets in a domatic partition of a graph ...

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.

The average power of a complex signal f(t) as a function of time t is defined as <f^2(t)>=lim_(T->infty)1/(2T)int_(-T)^T|f(t)|^2dt, where |z| is the complex modulus (Papoulis ...

A complex map is a map f:C->C. The following table lists several common types of complex maps. map formula domain complex magnification f(z)=az a in R, a>0 complex rotation ...

An expansion based on the roots of x^(-n)[xJ_n^'(x)+HJ_n(x)]=0, where J_n(x) is a Bessel function of the first kind, is called a Dini expansion.

The Doppler spiral is the curve obtained from an Archimedes' spiral which is translated horizontally with speed k. It has parametric equations x(t) = a(tcost+kt) (1) y(t) = ...