Search Results for ""

Let p be an odd prime, a be a positive number such that pa (i.e., p does not divide a), and let x be one of the numbers 1, 2, 3, ..., p-1. Then there is a unique x^', called ...

A Sheffer sequence for (1,f(t)) is called the associated sequence for f(t), and a sequence s_n(x) of polynomials satisfying the orthogonality conditions ...

The three circular triangles A^'B^'C^', AB^'C^', A^'BC^', and A^'B^'C obtained by extending the arcs of a circular triangle ABC into complete circles.

A sequence {x_n} is called an infinitive sequence if, for every i, x_n=i for infinitely many n. Write a(i,j) for the jth index n for which x_n=i. Then as i and j range ...

For an algebra A, the associator is the trilinear map A×A×A->A given by (x,y,z)=(xy)z-x(yz). The associator is identically zero iff A is associative.

The asterisk *, also called a "star," is used for a number of different purposed in mathematics. The most common usage is to denote multiplication so, for example, 2*3=2×3=6. ...

In general, the catacaustics of the astroid are complicated curves. For an astroid with parametric equations x = cos^3t (1) y = sin^3t, (2) the catacaustic for a radiant ...

The evolute of the astroid is a hypocycloid evolute for n=4. Surprisingly, it is another astroid scaled by a factor n/(n-2)=4/2=2 and rotated 1/(2·4)=1/8 of a turn. For an ...

The involute of the astroid is a hypocycloid involute for n=4. Surprisingly, it is another astroid scaled by a factor (n-2)/n=2/4=1/2 and rotated 1/(2·4)=1/8 of a turn. For ...

An asymmetric matrix is a square matrix that is not symmetric, i.e., a matrix A such that A^(T)!=A, where A^(T) denotes the transpose. An asymmetric matrix therefore ...