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Code 2040 is a totalistic cellular automaton that yields patterns with seemingly random features. The rules and 300 steps of this automaton are illustrated above.

Code 912 is a totalistic cellular automaton that yields patterns with seemingly random features. The rules and 300 steps of this automaton are illustrated above.

The look and say sequence generated from a starting digit of 3, as given by Vardi (1991).

A lag system, introduced by Wang (1963), is a sort of opposite to a tag system. Lag systems allow dependence on more than just the first element, but remove only the first ...

Any of the three standard forms in which an elliptic integral can be expressed.

1. Zero is a number. 2. If a is a number, the successor of a is a number. 3. zero is not the successor of a number. 4. Two numbers of which the successors are equal are ...

Let Gamma(z) be the gamma function and n!! denote a double factorial, then [(Gamma(m+1/2))/(Gamma(m))]^2[1/m+(1/2)^21/(m+1)+((1·3)/(2·4))^21/(m+2)+...]_()_(n) ...

If a contour in the complex plane is curved such that it separates the increasing and decreasing sequences of poles, then ...

If f(z) is regular and of the form O(e^(k|z|)) where k<pi, for R[z]>=0, and if f(z)=0 for z=0, 1, ..., then f(z) is identically zero.

The orthogonal polynomials defined by h_n^((alpha,beta))(x,N)=((-1)^n(N-x-n)_n(beta+x+1)_n)/(n!) ×_3F_2(-n,-x,alpha+N-x; N-x-n,-beta-x-n;1) =((-1)^n(N-n)_n(beta+1)_n)/(n!) ...