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A general type of statistical distribution which is related to the gamma distribution. Beta distributions have two free parameters, which are labeled according to one of two ...

A special case of Hölder's sum inequality with p=q=2, (sum_(k=1)^na_kb_k)^2<=(sum_(k=1)^na_k^2)(sum_(k=1)^nb_k^2), (1) where equality holds for a_k=cb_k. The inequality is ...

Clausen's integral, sometimes called the log sine integral (Borwein and Bailey 2003, p. 88) is the n=2 case of the S_2 Clausen function Cl_2(theta) = ...

The term "continued fraction" is used to refer to a class of expressions of which generalized continued fraction of the form b_0+(a_1)/(b_1+(a_2)/(b_2+(a_3)/(b_3+...))) ...

A cyclic number is an (n-1)-digit integer that, when multiplied by 1, 2, 3, ..., n-1, produces the same digits in a different order. Cyclic numbers are generated by the full ...

There are several types of integrals which go under the name of a "Dirichlet integral." The integral D[u]=int_Omega|del u|^2dV (1) appears in Dirichlet's principle. The ...

Euler (1772ab) conjectured that there are no positive integer solutions to the quartic Diophantine equation A^4=B^4+C^4+D^4. This conjecture was disproved by Elkies (1988), ...

A rational number expressed in the form a/b (in-line notation) or a/b (traditional "display" notation), where a is called the numerator and b is called the denominator. When ...

The geometric mean of a sequence {a_i}_(i=1)^n is defined by G(a_1,...,a_n)=(product_(i=1)^na_i)^(1/n). (1) Thus, G(a_1,a_2) = sqrt(a_1a_2) (2) G(a_1,a_2,a_3) = ...

A geometric series sum_(k)a_k is a series for which the ratio of each two consecutive terms a_(k+1)/a_k is a constant function of the summation index k. The more general case ...