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The decimal expansion of the Glaisher-Kinkelin constant is given by A=1.28242712... (OEIS A074962). A was computed to 5×10^5 decimal digits by E. Weisstein (Dec. 3, 2015). ...

A pair of primes (p,q) that sum to an even integer 2n=p+q are known as a Goldbach partition (Oliveira e Silva). Letting r(2n) denote the number of Goldbach partitions of 2n ...

The decimal expansion of the Golomb-Dickman constant is given by lambda=0.6243299885... (OEIS A084945). Mitchell (1968) computed lambda to 53 decimal places. lambda has been ...

An algorithm for finding closed form hypergeometric identities. The algorithm treats sums whose successive terms have ratios which are rational functions. Not only does it ...

Given any tree T having v vertices of vertex degrees of 1 and 3 only, form an n-expansion by taking n disjoint copies of T and joining corresponding leaves by an n-cycle ...

For an integer n>=2, let gpf(x) denote the greatest prime factor of n, i.e., the number p_k in the factorization n=p_1^(a_1)...p_k^(a_k), with p_i<p_j for i<j. For n=2, 3, ...

In celestial mechanics, the fixed path a planet traces as it moves around the sun is called an orbit. When a group G acts on a set X (this process is called a group action), ...

The unique (modulo rotations) scalene triangle formed from three vertices of a regular heptagon, having vertex angles pi/7, 2pi/7, and 4pi/7. There are a number of amazing ...

A second-order linear Hermitian operator is an operator L^~ that satisfies int_a^bv^_L^~udx=int_a^buL^~v^_dx. (1) where z^_ denotes a complex conjugate. As shown in ...

Let there be n ways for a "good" selection and m ways for a "bad" selection out of a total of n+m possibilities. Take N samples and let x_i equal 1 if selection i is ...