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The generalized hypergeometric function is given by a hypergeometric series, i.e., a series for which the ratio of successive terms can be written ...

Geometry is the study of figures in a space of a given number of dimensions and of a given type. The most common types of geometry are plane geometry (dealing with objects ...

The greatest common divisor, sometimes also called the highest common divisor (Hardy and Wright 1979, p. 20), of two positive integers a and b is the largest divisor common ...

A hyperbola (plural "hyperbolas"; Gray 1997, p. 45) is a conic section defined as the locus of all points P in the plane the difference of whose distances r_1=F_1P and ...

Let x be a real number, and let R be the set of positive real numbers mu for which 0<|x-p/q|<1/(q^mu) (1) has (at most) finitely many solutions p/q for p and q integers. Then ...

Let x=[a_0;a_1,...]=a_0+1/(a_1+1/(a_2+1/(a_3+...))) (1) be the simple continued fraction of a "generic" real number x, where the numbers a_i are the partial denominator. ...

In his last letter to Hardy, Ramanujan defined 17 Jacobi theta function-like functions F(q) with |q|<1 which he called "mock theta functions" (Watson 1936ab, Ramanujan 1988, ...

The Möbius-Kantor graph is the unique cubic symmetric graph on 16 nodes, illustrated above in several embeddings. Its unique canonical LCF notation is [5,-5]^8. The ...

Multiply all the digits of a number n by each other, repeating with the product until a single digit is obtained. The number of steps required is known as the multiplicative ...

The Newton-Cotes formulas are an extremely useful and straightforward family of numerical integration techniques. To integrate a function f(x) over some interval [a,b], ...