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Kepler's equation gives the relation between the polar coordinates of a celestial body (such as a planet) and the time elapsed from a given initial point. Kepler's equation ...

The number of equivalent hyperspheres in n dimensions which can touch an equivalent hypersphere without any intersections, also sometimes called the Newton number, contact ...

The logarithmic integral (in the "American" convention; Abramowitz and Stegun 1972; Edwards 2001, p. 26), is defined for real x as li(x) = {int_0^x(dt)/(lnt) for 0<x<1; ...

The logarithmic spiral is a spiral whose polar equation is given by r=ae^(btheta), (1) where r is the distance from the origin, theta is the angle from the x-axis, and a and ...

Calculus of variations can be used to find the curve from a point (x_1,y_1) to a point (x_2,y_2) which, when revolved around the x-axis, yields a surface of smallest surface ...

The product of primes p_n#=product_(k=1)^np_k, (1) with p_n the nth prime, is called the primorial function, by analogy with the factorial function. Its logarithm is closely ...

If A moves along a known curve, then P describes a pursuit curve if P is always directed toward A and A and P move with uniform velocities. Pursuit curves were considered in ...

Two integers are relatively prime if they share no common positive factors (divisors) except 1. Using the notation (m,n) to denote the greatest common divisor, two integers m ...

An ordinary differential equation of the form y^('')+P(x)y^'+Q(x)y=0. (1) Such an equation has singularities for finite x=x_0 under the following conditions: (a) If either ...

The Ulam sequence {a_i}=(u,v) is defined by a_1=u, a_2=v, with the general term a_n for n>2 given by the least integer expressible uniquely as the sum of two distinct earlier ...