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A number b_(2n) having generating function sum_(n=0)^(infty)b_(2n)x^(2n) = 1/2ln((e^(x/2)-e^(-x/2))/(1/2x)) (1) = 1/2ln2+1/(48)x^2-1/(5760)x^4+1/(362880)x^6-.... (2) For n=1, ...

A linear equation is an algebraic equation of the form y=mx+b involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept. The ...

The exterior derivative of a function f is the one-form df=sum_(i)(partialf)/(partialx_i)dx_i (1) written in a coordinate chart (x_1,...,x_n). Thinking of a function as a ...

The polynomials in the diagonal of the Smith normal form or rational canonical form of a matrix are called its invariant factors.

The Earls sequence gives the starting position in the decimal digits of pi (or in general, any constant), not counting digits to the left of the decimal point, at which a ...

A complex line bundle is a vector bundle pi:E->M whose fibers pi^(-1)(m) are a copy of C. pi is a holomorphic line bundle if it is a holomorphic map between complex manifolds ...

Self-recursion is a recursion that is defined in terms of itself, resulting in an ill-defined infinite regress. The formula for the volume of a cylinder leads to the ...

The tetragonal antiwedge is the topological class of hexahedron. It has 10 edges and 6 vertices and its faces consist of 4 triangles and 2 quadrilaterals. A tetragonal ...

The constant e is base of the natural logarithm. e is sometimes known as Napier's constant, although its symbol (e) honors Euler. e is the unique number with the property ...

Any sum of a selection of Pi_ks, where Pi_k denotes a k-D polytope.