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Roman (1984, p. 2) describes umbral calculus as the study of the class of Sheffer sequences. Umbral calculus provides a formalism for the systematic derivation and ...

A variable is a symbol on whose value a function, polynomial, etc., depends. For example, the variables in the function f(x,y) are x and y. A function having a single ...

The series h_q(-r)=sum_(n=1)^infty1/(q^n+r) (1) for q an integer other than 0 and +/-1. h_q and the related series Ln_q(-r+1)=sum_(n=1)^infty((-1)^n)/(q^n+r), (2) which is a ...

A die (plural "dice") is a solid with markings on each of its faces. The faces are usually all the same shape, making Platonic solids and Archimedean duals the obvious ...

Pascal's triangle is a number triangle with numbers arranged in staggered rows such that a_(nr)=(n!)/(r!(n-r)!)=(n; r), (1) where (n; r) is a binomial coefficient. The ...

A clique of a graph G is a complete subgraph of G, and the clique of largest possible size is referred to as a maximum clique (which has size known as the (upper) clique ...

Bridge is a card game played with a normal deck of 52 cards. The number of possible distinct 13-card hands is N=(52; 13)=635013559600, (1) where (n; k) is a binomial ...

A differential k-form is a tensor of tensor rank k that is antisymmetric under exchange of any pair of indices. The number of algebraically independent components in n ...

The distance between two points is the length of the path connecting them. In the plane, the distance between points (x_1,y_1) and (x_2,y_2) is given by the Pythagorean ...

The falling factorial (x)_n, sometimes also denoted x^(n__) (Graham et al. 1994, p. 48), is defined by (x)_n=x(x-1)...(x-(n-1)) (1) for n>=0. Is also known as the binomial ...