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If f_1,...,f_m:R^n->R are exponential polynomials, then {x in R^n:f_1(x)=...f_n(x)=0} has finitely many connected components.

The equation defining Killing vectors. L_Xg_(ab)=X_(a;b)+X_(b;a)=2X_((a;b))=0, where L is the Lie derivative and X_(b;a) is a covariant derivative.

The system of partial differential equations del ^2s-(|a|^2+1)s = 0 (1) del ^2a-del (del ·a)-s^2a = a. (2)

The infinite product identity Gamma(1+v)=2^(2v)product_(m=1)^infty[pi^(-1/2)Gamma(1/2+2^(-m)v)], where Gamma(x) is the gamma function.

Let J_nu(z) be a Bessel function of the first kind, N_nu(z) a Bessel function of the second kind, and j_(nu,n)(z) the zeros of z^(-nu)J_nu(z) in order of ascending real part. ...

A theorem which states that if a Kähler form represents an integral cohomology class on a compact manifold, then it must be a projective Abelian variety.

If an analytic function has a single simple pole at the radius of convergence of its power series, then the ratio of the coefficients of its power series converges to that ...

The forward and inverse Kontorovich-Lebedev transforms are defined by K_(ix)[f(t)] = int_0^inftyK_(ix)(t)f(t)dt (1) K_(ix)^(-1)[g(t)] = ...

The partial differential equation u_t+2uu_x-nuu_(xx)+muu_(xxx)=0.

The system of ordinary differential equations (dm)/(dt) = lambdamxm+gammax1 (1) (dgamma)/(dt) = lambdagammaxm. (2)