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The harmonic mean H(x_1,...,x_n) of n numbers x_i (where i=1, ..., n) is the number H defined by 1/H=1/nsum_(i=1)^n1/(x_i). (1) The harmonic mean of a list of numbers may be ...

The distinct prime factors of a positive integer n>=2 are defined as the omega(n) numbers p_1, ..., p_(omega(n)) in the prime factorization ...

The base-3 method of counting in which only the digits 0, 1, and 2 are used. Ternary numbers arise in a number of problems in mathematics, including some problems of ...

The Owen T-function is defined as T(x,a)=1/(2pi)int_0^a(e^(-x^2(1+t^2)/2))/(1+t^2)dt. It is implemented in the Wolfram Language as OwenT[x, a]. A special value is given by ...

Half-angle formulas and formulas expressing trigonometric functions of an angle x/2 in terms of functions of an angle x. For real x, sin(1/2x) = ...

Campbell (2022) used the WZ method to obtain the sum (pi^2)/4=sum_(n=1)^infty(16^n(n+1)(3n+1))/(n(2n+1)^2(2n; n)^3), (1) where (n; k) is a binomial coefficient. There is a ...

Let {A_n}_(n=0)^infty be a sequence of events occurring with a certain probability distribution, and let A be the event consisting of the occurrence of a finite number of ...

A sequence {nu_i} of nondecreasing positive integers is complete iff 1. nu_1=1. 2. For all k=2, 3, ..., s_(k-1)=nu_1+nu_2+...+nu_(k-1)>=nu_k-1. A corollary states that a ...

Given a Lyapunov characteristic exponent sigma_i, the corresponding Lyapunov characteristic number lambda_i is defined as lambda_i=e^(sigma_i). (1) For an n-dimensional ...

An integer sequence given by the recurrence relation a(n)=a(a(n-2))+a(n-a(n-2)) with a(1)=a(2)=1. The first few values are 1, 1, 2, 3, 3, 4, 5, 6, 6, 7, 7, 8, 9, 10, 10, 11, ...