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The quaternions are members of a noncommutative division algebra first invented by William Rowan Hamilton. The idea for quaternions occurred to him while he was walking along ...

The quintuple product identity, also called the Watson quintuple product identity, states (1) It can also be written (2) or (3) The quintuple product identity can be written ...

The Radon-Nikodym theorem asserts that any absolutely continuous complex measure lambda with respect to some positive measure mu (which could be Lebesgue measure or Haar ...

Oloa (2010, pers. comm., Jan. 20, 2010) has considered the following integrals containing nested radicals of 1/2 plus terms in theta^2 and ln^2costheta: R_n^- = (1) R_n^+ = ...

Suppose that in some neighborhood of x=0, F(x)=sum_(k=0)^infty(phi(k)(-x)^k)/(k!) (1) for some function (say analytic or integrable) phi(k). Then ...

The ramp function is defined by R(x) = xH(x) (1) = int_(-infty)^xH(x^')dx^' (2) = int_(-infty)^inftyH(x^')H(x-x^')dx^' (3) = H(x)*H(x), (4) where H(x) is the Heaviside step ...

By analogy with the squircle, a term first apparently used by Fernández Guasti et al. (2005), the term "rectellipse" (used here for the first time) is a natural ...

The reflection circle, a term coined here for the first time, is the circumcircle of the reflection triangle. It has center at Kimberling center X_(195), which is the ...

A repeated integral is an integral taken multiple times over a single variable (as distinguished from a multiple integral, which consists of a number of integrals taken with ...

Also called "Ethiopian multiplication." To multiply two numbers a and b, write a_0=a and b_0=b in two columns. Under a_0, write |_a_0/2_|, where |_x_| is the floor function, ...