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Let f be an entire function of finite order lambda and {a_j} the zeros of f, listed with multiplicity, then the rank p of f is defined as the least positive integer such that ...

The equations defined by q^. = (partialH)/(partialp) (1) p^. = -(partialH)/(partialq), (2) where p^.=dp/dt and q^.=dq/dt is fluxion notation and H is the so-called ...

In music, if a note has frequency f, integer multiples of that frequency, 2f,3f,4f and so on, are known as harmonics. As a result, the mathematical study of overlapping waves ...

The haversine, also called the haversed sine, is a little-used entire trigonometric function defined by hav(z) = 1/2vers(z) (1) = 1/2(1-cosz) (2) = sin^2(1/2z), (3) where ...

The nontrivial zeros of the Riemann zeta function correspond to the eigenvalues of some Hermitian operator (Derbyshire 2004, pp. 277-278).

The bifurcation of a fixed point to a limit cycle (Tabor 1989).

Horowitz reduction is used in indefinite integration to reduce a rational function into polynomial and logarithmic parts. The polynomial part is then trivially integrated, ...

The expected value B_n(s) of r^s from a fixed vertex of a unit n-cube to a point picked at random in the interior of the hypercube is given by B_n(s) = ...

The hyperfactorial (Sloane and Plouffe 1995) is the function defined by H(n) = K(n+1) (1) = product_(k=1)^(n)k^k, (2) where K(n) is the K-function. The hyperfactorial is ...

An improper integral is a definite integral that has either or both limits infinite or an integrand that approaches infinity at one or more points in the range of ...