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product_(k=1)^(n)(1+yq^k) = sum_(m=0)^(n)y^mq^(m(m+1)/2)[n; m]_q (1) = sum_(m=0)^(n)y^mq^(m(m+1)/2)((q)_n)/((q)_m(q)_(n-m)), (2) where [n; m]_q is a q-binomial coefficient.

A complex map is a map f:C->C. The following table lists several common types of complex maps. map formula domain complex magnification f(z)=az a in R, a>0 complex rotation ...

A variable that may assume complex values.

A map f:X-->Y is called constant with constant value y if f(x)=y for all x in X, i.e., if all elements of X are sent to same element y of Y.

int_0^inftye^(-omegaT)cos(omegat)domega=T/(t^2+T^2), which can be computed using integration by parts.

Given a Jacobi amplitude phi and a elliptic modulus m in an elliptic integral, Delta(phi)=sqrt(1-msin^2phi).

The Dirichlet kernel D_n^M is obtained by integrating the number theoretic character e^(i<xi,x>) over the ball |xi|<=M, D_n^M=-1/(2pir)d/(dr)D_(n-2)^M.

int_0^pi(sin[(n+1/2)x])/(2sin(1/2x))dx=1/2pi, where the integral kernel is the Dirichlet kernel.

The second singular value k_2, corresponding to K^'(k_2)=sqrt(2)K(k_2), (1) is given by k_2 = tan(pi/8) (2) = sqrt(2)-1 (3) k_2^' = sqrt(2)(sqrt(2)-1). (4) For this modulus, ...

An exponent is the power p in an expression of the form a^p. The process of performing the operation of raising a base to a given power is known as exponentiation.