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There are (at least) three types of Euler transforms (or transformations). The first is a set of transformations of hypergeometric functions, called Euler's hypergeometric ...

Consider the Euler product zeta(s)=product_(k=1)^infty1/(1-1/(p_k^s)), (1) where zeta(s) is the Riemann zeta function and p_k is the kth prime. zeta(1)=infty, but taking the ...

Rubik's Cube is a 3×3×3 cube in which the 26 subcubes on the outside are internally hinged in such a way that rotation (by a quarter turn in either direction or a half turn) ...

The Euclidean algorithm, also called Euclid's algorithm, is an algorithm for finding the greatest common divisor of two numbers a and b. The algorithm can also be defined for ...

Take x itself to be a bracketing, then recursively define a bracketing as a sequence B=(B_1,...,B_k) where k>=2 and each B_i is a bracketing. A bracketing can be represented ...

Let the difference of successive primes be defined by d_n=p_(n+1)-p_n, and d_n^k by d_n^k={d_n for k=1; |d_(n+1)^(k-1)-d_n^(k-1)| for k>1. (1) N. L. Gilbreath claimed that ...

The function intx gives the integer part of x. In many computer languages, the function is denoted int(x). It is related to the floor and ceiling functions |_x_| and [x] by ...

Cubic lattice sums include the following: b_2(2s) = sum^'_(i,j=-infty)^infty((-1)^(i+j))/((i^2+j^2)^s) (1) b_3(2s) = ...

Mills' theorem states that there exists a real constant A such that |_A^(3^n)_| is prime for all positive integers n (Mills 1947). While for each value of c>=2.106, there are ...

A function is said to be modular (or "elliptic modular") if it satisfies: 1. f is meromorphic in the upper half-plane H, 2. f(Atau)=f(tau) for every matrix A in the modular ...