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The system of partial differential equations u_t = (u^2-u_x+2v)_x (1) v_y = (2uv+v_x)_x. (2)

A dynamical system in which the phase space volume contracts along a trajectory. This means that the generalized divergence is less than zero, (partialf_i)/(partialx_i)<0, ...

The distribution parameter of a noncylindrical ruled surface parameterized by x(u,v)=sigma(u)+vdelta(u), (1) where sigma is the striction curve and delta the director curve, ...

sum_(k=-n)^n(-1)^k(n+b; n+k)(n+c; c+k)(b+c; b+k)=(Gamma(b+c+n+1))/(n!Gamma(b+1)Gamma(c+1)), where (n; k) is a binomial coefficient and Gamma(x) is a gamma function.

y=delta^'(x-a), where delta(x) is the delta function.

For R[a+b-c-d]<-1 and a and b not integers,

The system of partial differential equations u_t = 3ww_x (1) w_t = 2w_(xxx)+2uw_x+u_xw. (2)

The Eberlein polynomials of degree 2k and variable x are the orthogonal polynomials arising in the Johnson scheme that may be defined by E_k^((n,v))(x) = ...

The second-order ordinary differential equation y^('')+[(alphaeta)/(1+eta)+(betaeta)/((1+eta)^2)+gamma]y=0, where eta=e^(deltax).

A proof which can be accomplished using only real numbers (i.e., real analysis instead of complex analysis; Hoffman 1998, pp. 92-93).