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Define the notation [n]f_0=f_(-(n-1)/2)+...+f_0+...+f_((n-1)/2) (1) and let delta be the central difference, so delta^2f_0=f_1-2f_0+f_(-1). (2) Spencer's 21-term moving ...

The duplication formula for Rogers L-function follows from Abel's functional equation and is given by 1/2L(x^2)=L(x)-L(x/(1+x)).

A Mrs. Perkins's quilt is a dissection of a square of side n into a number of smaller squares. The name "Mrs. Perkins's Quilt" comes from a problem in one of Dudeney's books, ...

The Johnson solids are the convex polyhedra having regular faces and equal edge lengths (with the exception of the completely regular Platonic solids, the "semiregular" ...

A set S in a metric space (S,d) is bounded if it has a finite generalized diameter, i.e., there is an R<infty such that d(x,y)<=R for all x,y in S. A set in R^n is bounded ...

A particular solution to a differential equation corresponding to a specific value of the equation's free parameters. For example, the integral curves of the differential ...

The projective special linear group PSL_n(q) is the group obtained from the special linear group SL_n(q) on factoring by the scalar matrices contained in that group. It is ...

An integral of the form intf(z)dz, (1) i.e., without upper and lower limits, also called an antiderivative. The first fundamental theorem of calculus allows definite ...

The term Mandelbrot set is used to refer both to a general class of fractal sets and to a particular instance of such a set. In general, a Mandelbrot set marks the set of ...

The simple continued fraction for pi is given by [3; 7, 15, 1, 292, 1, 1, 1, 2, 1, 3, 1, 14, 2, 1, 1, 2, 2, 2, 2, ...] (OEIS A001203). A plot of the first 256 terms of the ...