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Ai(z) and Ai^'(z) have zeros on the negative real axis only. Bi(z) and Bi^'(z) have zeros on the negative real axis and in the sector pi/3<|argz|<pi/2. The nth (real) roots ...

Consider a game, first proposed by Nicolaus Bernoulli, in which a player bets on how many tosses of a coin will be needed before it first turns up heads. The player pays a ...

An array of "trees" of unit height located at integer-coordinate points in a point lattice. When viewed from a corner along the line y=x in normal perspective, a quadrant of ...

A transformation from one reference frame to another moving with a constant velocity v with respect to the first for classical motion. However, special relativity shows that ...

In above figure, which constitutes a modified version of the painting Tirets by Francois Morellet, small circles seem to appear and disappear as the eye is moved over them.

Let p be an odd prime, k be an integer such that pk and 1<=k<=2(p+1), and N=2kp+1. Then the following are equivalent 1. N is prime. 2. There exists an a such that ...

A notation for large numbers defined by Steinhaus (1983, pp. 28-29). In this notation, denotes n^n, denotes "n in n triangles," and denotes "n in n squares." A modified ...

The engineering terminology for one use of Fourier transforms. By breaking up a wave pulse into its frequency spectrum f_nu=F(nu)e^(2piinut), (1) the entire signal can be ...

Let c and d!=c be real numbers (usually taken as c=1 and d=0). The Dirichlet function is defined by D(x)={c for x rational; d for x irrational (1) and is discontinuous ...

A generalized Fourier series is a series expansion of a function based on the special properties of a complete orthogonal system of functions. The prototypical example of ...