Search Results for ""

A Taylor series is a series expansion of a function about a point. A one-dimensional Taylor series is an expansion of a real function f(x) about a point x=a is given by (1) ...

A continuous transformation from one function to another. A homotopy between two functions f and g from a space X to a space Y is a continuous map G from X×[0,1]|->Y such ...

A relation connecting the values of a meromorphic function inside a disk with its boundary values on the circumference and with its zeros and poles (Jensen 1899, Levin 1980). ...

Each Cartan matrix determines a unique semisimple complex Lie algebra via the Chevalley-Serre, sometimes called simply the "Serre relations." That is, if (A_(ij)) is a k×k ...

The cross-correlation of two complex functions f(t) and g(t) of a real variable t, denoted f*g is defined by f*g=f^_(-t)*g(t), (1) where * denotes convolution and f^_(t) is ...

A field automorphism of a field F is a bijective map sigma:F->F that preserves all of F's algebraic properties, more precisely, it is an isomorphism. For example, complex ...

The natural logarithm lnx is the logarithm having base e, where e=2.718281828.... (1) This function can be defined lnx=int_1^x(dt)/t (2) for x>0. This definition means that e ...

An even Mathieu function ce_r(z,q) with characteristic value a_r.

A mathematical relationship transforming a function f(x) to the form f(x+a).

An elliptic integral is an integral of the form int(A(x)+B(x)sqrt(S(x)))/(C(x)+D(x)sqrt(S(x)))dx, (1) or int(A(x)dx)/(B(x)sqrt(S(x))), (2) where A(x), B(x), C(x), and D(x) ...