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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 complexity of a pattern parameterized as the shortest algorithm required to reproduce it. Also known as bit complexity.

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)

The partial differential equation P_t=P_(xx)-uP_x+partial/(partialx){[u-F(x)]P}.

The symbol defined by c^(a/b) = c(c+b)(c+2b)...[c+(a-1)b] (1) = b^a(c/b)_a (2) = (b^aGamma(a+c/b))/(Gamma(c/b)), (3) where (a)_n is the Pochhammer symbol and Gamma(z) is the ...

The Kronecker sum is the matrix sum defined by A direct sum B=A tensor I_b+I_a tensor B, (1) where A and B are square matrices of order a and b, respectively, I_n is the ...

A polynomial factorization algorithm that proceeds by considering the vector of coefficients of a polynomial P, calculating b_i=P(i)/a_i, constructing the Lagrange ...

A generalization of the Wilcoxon rank sum test.