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A number is said to be squarefree (or sometimes quadratfrei; Shanks 1993) if its prime decomposition contains no repeated factors. All primes are therefore trivially ...

If F(x) is a probability distribution with zero mean and rho=int_(-infty)^infty|x|^3dF(x)<infty, (1) where the above integral is a stieltjes integral, then for all x and n, ...

A sieving procedure that can be used in conjunction with Dixon's factorization method to factor large numbers n. Pick values of r given by r=|_sqrt(n)_|+k, (1) where k=1, 2, ...

A function f is Carathéodory differentiable at a if there exists a function phi which is continuous at a such that f(x)-f(a)=phi(x)(x-a). Every function which is Carathéodory ...

An even Mathieu function ce_r(z,q) with characteristic value a_r.

A mathematical relationship transforming a function f(x) to the form f(x+a).

The word argument is used in several differing contexts in mathematics. The most common usage refers to the argument of a function, but is also commonly used to refer to the ...

An equation derived by Kronecker: where r(n) is the sum of squares function, zeta(z) is the Riemann zeta function, eta(z) is the Dirichlet eta function, Gamma(z) is the gamma ...

Wirsing (1974) showed, among other results, that if F_n(x) is the Gauss-Kuzmin distribution, then lim_(n->infty)(F_n(x)-lg(1+x))/((-lambda)^n)=Psi(x), (1) where ...

A function for which the integral can be computed is said to be integrable.