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A technique used by André (1887) to provide an elegant solution to the ballot problem (Hilton and Pederson 1991) and in study of Wiener processes (Doob 1953; Papoulis 1984, ...

The exponent laws, also called the laws of indices (Higgens 1998) or power rules (Derbyshire 2004, p. 65), are the rules governing the combination of exponents (powers). The ...

A number given by the generating function (2t)/(e^t+1)=sum_(n=1)^inftyG_n(t^n)/(n!). (1) It satisfies G_1=1, G_3=G_5=G_7=...=0, and even coefficients are given by G_(2n) = ...

Goldberg polyhedra are convex polyhedra first described by Goldberg (1937) and classified in more detail by Hart (2013) for which each face is a regular pentagon or regular ...

A complicated polynomial root-finding algorithm which is used in the IMSL® (IMSL, Houston, TX) library and which Press et al. (1992) describe as "practically a standard in ...

For n>=1, let u and v be integers with u>v>0 such that the Euclidean algorithm applied to u and v requires exactly n division steps and such that u is as small as possible ...

A method for finding roots which defines P_j(x)=(P(x))/((x-x_1)...(x-x_j)), (1) so the derivative is (2) One step of Newton's method can then be written as ...

The consideration of the result of a numerical calculation as a function of an adjustable parameter (usually the step size). The function can then be fitted and evaluated at ...

A powerful numerical integration technique which uses k refinements of the extended trapezoidal rule to remove error terms less than order O(N^(-2k)). The routine advocated ...

An algorithm for multiplying two 32-bit integers modulo a 32-bit constant without using any intermediates larger than 32 bits. It is also useful in certain types of random ...