Search Results for ""

Apéry's constant is defined by zeta(3)=1.2020569..., (1) (OEIS A002117) where zeta(z) is the Riemann zeta function. Apéry (1979) proved that zeta(3) is irrational, although ...

A definite integral is an integral int_a^bf(x)dx (1) with upper and lower limits. If x is restricted to lie on the real line, the definite integral is known as a Riemann ...

A general prism is a polyhedron possessing two congruent polygonal faces and with all remaining faces parallelograms (Kern and Bland 1948, p. 28; left figure). A right prism ...

The anticomplementary triangle is the triangle DeltaA_1^'A_2^'A_3^' which has a given triangle DeltaA_1A_2A_3 as its medial triangle. It is therefore the anticevian triangle ...

Bridge is a card game played with a normal deck of 52 cards. The number of possible distinct 13-card hands is N=(52; 13)=635013559600, (1) where (n; k) is a binomial ...

The Cassini ovals are a family of quartic curves, also called Cassini ellipses, described by a point such that the product of its distances from two fixed points a distance ...

The confluent hypergeometric function of the second kind gives the second linearly independent solution to the confluent hypergeometric differential equation. It is also ...

A cylindrical wedge, also called a cylindrical hoof or cylindrical ungula, is a wedge cut from a cylinder by slicing with a plane that intersects the base of the cylinder. ...

Let the divisor function d(n) be the number of divisors of n (including n itself). For a prime p, d(p)=2. In general, sum_(k=1)^nd(k)=nlnn+(2gamma-1)n+O(n^theta), where gamma ...

If x_0 is an ordinary point of the ordinary differential equation, expand y in a Taylor series about x_0. Commonly, the expansion point can be taken as x_0=0, resulting in ...