Search Results for ""

The nesting of two or more functions to form a single new function is known as composition. The composition of two functions f and g is denoted f degreesg, where f is a ...

The sine function sinx is one of the basic functions encountered in trigonometry (the others being the cosecant, cosine, cotangent, secant, and tangent). Let theta be an ...

The distribution of the product X_1X_2...X_n of n uniform variates on the interval [0,1] can be found directly as P_(X_1...X_n)(u) = ...

A hypergeometric identity discovered by Ramanujan around 1910. From Hardy (1999, pp. 13 and 102-103), (1) where a^((n))=a(a+1)...(a+n-1) (2) is the rising factorial (a.k.a. ...

The Jacobi triple product is the beautiful identity product_(n=1)^infty(1-x^(2n))(1+x^(2n-1)z^2)(1+(x^(2n-1))/(z^2))=sum_(m=-infty)^inftyx^(m^2)z^(2m). (1) In terms of the ...

The word argument is used in several differing contexts in mathematics. The most common usage refers to the argument of a function, but is also commonly used to refer to the ...

An algorithm which finds a polynomial recurrence for terminating hypergeometric identities of the form sum_(k)(n; ...

A square matrix with constant skew diagonals. In other words, a Hankel matrix is a matrix in which the (i,j)th entry depends only on the sum i+j. Such matrices are sometimes ...

Let G=(V,E) be a (not necessarily simple) undirected edge-weighted graph with nonnegative weights. A cut C of G is any nontrivial subset of V, and the weight of the cut is ...

There exists a positive integer s such that every sufficiently large integer is the sum of at most s primes. It follows that there exists a positive integer s_0>=s such that ...