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A beautiful approximation to the Euler-Mascheroni constant gamma is given by pi/(2e)=0.57786367... (1) (OEIS A086056; E. W. Weisstein, Apr. 18, 2006), which is good to three ...

Replacing the logistic equation (dx)/(dt)=rx(1-x) (1) with the quadratic recurrence equation x_(n+1)=rx_n(1-x_n), (2) where r (sometimes also denoted mu) is a positive ...

The number M_2(n) = 1/nsum_(k=1)^(n^2)k (1) = 1/2n(n^2+1) (2) to which the n numbers in any horizontal, vertical, or main diagonal line must sum in a magic square. The first ...

Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let phi(n) or phi(x) be a positive function and f(n) or ...

A spiral that gives the solution to the central orbit problem under a radial force law r^..=-mu|r|^(-3)r^^, (1) where mu is a positive constant. There are three solution ...

Critical damping is a special case of damped simple harmonic motion x^..+betax^.+omega_0^2x=0, (1) in which D=beta^2-4omega_0^2=0, (2) where beta is the damping constant. ...

The fibonorial n!_F, also called the Fibonacci factorial, is defined as n!_F=product_(k=1)^nF_k, where F_k is a Fibonacci number. For n=1, 2, ..., the first few fibonorials ...

A function phi(t) satisfies the Hölder condition on two points t_1 and t_2 on an arc L when |phi(t_2)-phi(t_1)|<=A|t_2-t_1|^mu, with A and mu positive real constants. In some ...

Consider the sequence {x_n}_(n=0)^infty defined by x_0=1 and x_(n+1)=[3/2x_n], where [z] is the ceiling function. For n=0, 1, ..., the first few terms are 1, 2, 3, 5, 8, 12, ...

In logic, a term is a variable, constant, or the result of acting on variables and constants by function symbols. In algebra, a term is a product of the form x^n (in the ...