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The union of two sets A and B is the set obtained by combining the members of each. This is written A union B, and is pronounced "A union B" or "A cup B." The union of sets ...

The orthogonal polynomials defined variously by (1) (Koekoek and Swarttouw 1998, p. 24) or p_n(x;a,b,c,d) = W_n(-x^2;a,b,c,d) (2) = (3) (Koepf, p. 116, 1998). The first few ...

Let the values of a function f(x) be tabulated at points x_i equally spaced by h=x_(i+1)-x_i, so f_1=f(x_1), f_2=f(x_2), ..., f_n=f(x_n). Then Woolhouse's formulas ...

When p is a prime number, then a p-group is a group, all of whose elements have order some power of p. For a finite group, the equivalent definition is that the number of ...

At rational arguments p/q, the digamma function psi_0(p/q) is given by psi_0(p/q)=-gamma-ln(2q)-1/2picot(p/qpi) +2sum_(k=1)^([q/2]-1)cos((2pipk)/q)ln[sin((pik)/q)] (1) for ...

A sextic graph is a regular graph of degree six. The numbers of simple sextic graphs on n=7, 8, ... nodes are 1, 1, 4, 21, 266, 7846, 367860, ... (OEIS A006822). Examples are ...

A cube 13-compound can be constructed as the dual of the octahedron 13-compound. It will be implemented in a future version of the Wolfram Language as ...

A octagrammic prism is a prism formed by two regular octagrams offset along their symmetry axis and with corresponding edges connected by lateral faces. For an equilateral ...

There are a number of attractive polyhedron compounds consisting of 13 octahedra. This compound will be implemented in a future version of the Wolfram Language as ...

The orthotomic of the unit circle represented by x = cost (1) y = sint (2) with a source at (x,y) is x_o = xcos(2t)-ysin(2t)+2sint (3) y_o = -xsin(2t)-ycos(2t)+2cost. (4)