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The vertex height of a vertex v in a rooted tree is the number of edges on the longest downward path between v and a tree leaf. The height of the root vertex of a rooted tree ...

The polynomials G_n(x;a,b) given by the associated Sheffer sequence with f(t)=e^(at)(e^(bt)-1), (1) where b!=0. The inverse function (and therefore generating function) ...

There are several types of integrals which go under the name of a "Dirichlet integral." The integral D[u]=int_Omega|del u|^2dV (1) appears in Dirichlet's principle. The ...

If there are two functions F_1(t) and F_2(t) with the same integral transform T[F_1(t)]=T[F_2(t)]=f(s), (1) then a null function can be defined by delta_0(t)=F_1(t)-F_2(t) ...

Let gamma(t) be a smooth curve in a manifold M from x to y with gamma(0)=x and gamma(1)=y. Then gamma^'(t) in T_(gamma(t)), where T_x is the tangent space of M at x. The ...

The Lerch transcendent is generalization of the Hurwitz zeta function and polylogarithm function. Many sums of reciprocal powers can be expressed in terms of it. It is ...

The vector Laplacian can be generalized to yield the tensor Laplacian A_(munu;lambda)^(;lambda) = (g^(lambdakappa)A_(munu;lambda))_(;kappa) (1) = ...

A real-valued univariate function f=f(x) has a jump discontinuity at a point x_0 in its domain provided that lim_(x->x_0-)f(x)=L_1<infty (1) and lim_(x->x_0+)f(x)=L_2<infty ...

A generalization of the polylogarithm function defined by S_(n,p)(z)=((-1)^(n+p-1))/((n-1)!p!)int_0^1((lnt)^(n-1)[ln(1-zt)]^p)/tdt. The function reduces to the usual ...

An unknown is an independent variable of a function. A function with n independent variables is said to be a function "in," "with," or "of" n unknowns.