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A sum which includes both the Jacobi triple product and the q-binomial theorem as special cases. Ramanujan's sum is ...

"The rationals" refers to the set of rational numbers and is commonly denoted Q.

"The reals" is a common way of referring to the set of real numbers and is commonly denoted R.

The reciprocal differences are closely related to the divided difference. The first few are explicitly given by rho(x_0,x_1)=(x_0-x_1)/(f_0-f_1) (1) ...

A reduced root system is a root system R satisfying the additional property that, if alpha in R, then the only multiples of alpha in R are +/-alpha.

The topology induced by a topological space X on a subset S. The open sets of S are the intersections S intersection U, where U is an open set of X. For example, in the ...

S_n(z) = zj_n(z)=sqrt((piz)/2)J_(n+1/2)(z) (1) C_n(z) = -zn_n(z)=-sqrt((piz)/2)N_(n+1/2)(z), (2) where j_n(z) and n_n(z) are spherical Bessel functions of the first and ...

A manifold possessing a metric tensor. For a complete Riemannian manifold, the metric d(x,y) is defined as the length of the shortest curve (geodesic) between x and y. Every ...

The problem of determining the vertices of a Schwarz-Christoffel mapping (Krantz 1999, p. 176).

The partial differential equation u_(xt)=sinhu, which contains u_(xt) instead of u_(xx)-u_(tt) and sinhu instead to sinu, as in the sine-Gordon equation (Grauel 1985; ...