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The mutual information between two discrete random variables X and Y is defined to be I(X;Y)=sum_(x in X)sum_(y in Y)P(x,y)log_2((P(x,y))/(P(x)P(y))) (1) bits. Additional ...

The identities between the symmetric polynomials Pi_k(x_1,...,x_n) and the sums of kth powers of their variables S_k(x_1,...,x_n)=sum_(j=1)^nx_j^k. (1) The identities are ...

Given a function f specified by parametric variables u_1, ..., u_n, a reparameterization f^^ of f over domain U is a change of variables u_i in U->v_i->V via a function phi ...

An expression which is a sentence or which contains variables and becomes a sentence upon appropriate substitutions for these variables (Carnap 1958, p. 24). Sentential ...

Summation by parts for discrete variables is the equivalent of integration by parts for continuous variables Delta^(-1)[v(x)Deltau(x)]=u(x)v(x)-Delta^(-1)[Eu(x)Deltav(x)], ...

The triangle coefficient is function of three variables written Delta(abc)=Delta(a,b,c) and defined by Delta(abc)=((a+b-c)!(a-b+c)!(-a+b+c)!)/((a+b+c+1)!), (Shore and Menzel ...

A universal sentence is a sentence (i.e., formula of the predicate calculus without free variables) whose variables are universally quantified.

Multivariable Calculus

The term "parameter" is used in a number of ways in mathematics. In general, mathematical functions may have a number of arguments. Arguments that are typically varied when ...

A formal extension of the hypergeometric function to two variables, resulting in four kinds of functions (Appell 1925; Picard 1880ab, 1881; Goursat 1882; Whittaker and Watson ...