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The variation of a function which exhibits slope changes, also called the saltus of a function. A series may also oscillate, causing it not to converge.

If x_1/n_1 and x_2/n_2 are the observed proportions from standard normally distributed samples with proportion of success theta, then the probability that ...

The term "over" is commonly used in mathematical exposition as a synonym for "in the domain of." So, for example, "Let f be a function over the reals" means "Let f be a ...

There are two definitions of Bernoulli polynomials in use. The nth Bernoulli polynomial is denoted here by B_n(x) (Abramowitz and Stegun 1972), and the archaic form of the ...

where _3F_2(a,b,c;d,e;z) is a generalized hypergeometric function and Gamma(z) is the gamma function (Bailey 1935, p. 16; Koepf 1998, p. 32).

The function K_n(x_0,x)=K_n(x,x_0)^_=K_n(x^_,x^__0) which is useful in the study of many polynomials.

A function used to study ordinary differential equations.

A smooth manifold with a Poisson bracket defined on its function space.

The set closure of the set of arguments of a function f for which f is not zero.

Let n be a positive number having primitive roots. If g is a primitive root of n, then the numbers 1, g, g^2, ..., g^(phi(n)-1) form a reduced residue system modulo n, where ...