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Lehmer's formula is a formula for the prime counting function, pi(x) = (1) where |_x_| is the floor function, a = pi(x^(1/4)) (2) b = pi(x^(1/2)) (3) b_i = pi(sqrt(x/p_i)) ...

A generalization of the product rule for expressing arbitrary-order derivatives of products of functions, where (n; k) is a binomial coefficient. This can also be written ...

A wavelet used in multiresolution representation to analyze the information content of images. The wavelet is defined by ...

A lens space L(p,q) is the 3-manifold obtained by gluing the boundaries of two solid tori together such that the meridian of the first goes to a (p,q)-curve on the second, ...

If there are two functions F_1(t) and F_2(t) with the same integral transform T[F_1(t)]=T[F_2(t)]=f(s), (1) then a null function can be defined by delta_0(t)=F_1(t)-F_2(t) ...

A quantity a is said to be less than b if a is smaller than b, written a<b. If a is less than or equal to b, the relationship is written a<=b. In the Wolfram Language, this ...

A method of displaying simple statistical parameters including hinges, the statistical median, and upper and lower values.

A letter is an element of an alphabet. A collection of letters forms a word.

Let t(m) denote the set of the phi(m) numbers less than and relatively prime to m, where phi(n) is the totient function. Then if S_m=sum_(t(m))1/t, (1) then {S_m=0 (mod m^2) ...

For a sequence {chi_i}, the Levine-O'Sullivan greedy algorithm is given by chi_1 = 1 (1) chi_i = max_(1<=j<=i-1)(j+1)(i-chi_j) (2) for i>1. The sequence generated by this ...