Search Results for ""

A function f(x) is absolutely monotonic in the interval a<x<b if it has nonnegative derivatives of all orders in the region, i.e., f^((k))(x)>=0 (1) for a<x<b and k=0, 1, 2, ...

Every finite-dimensional Lie algebra of characteristic p=0 has a faithful finite-dimensional representation.

A congruence of the form f(x)=0 (mod n) where f(x) is an integer polynomial (Nagell 1951, p. 73).

The function psi(x)={sin(x/c) |x|<cpi; 0 |x|>cpi, (1) which occurs in estimation theory.

For homogeneous polynomials P and Q of degree n, [P,Q]=sum_(i_1,...,i_n>=0)(i_1!...i_n!)(a_(i,...,i_n)b_(i_1,...,i_n)).

The partial differential equation u_(xxx)-1/8u_x^3+u_x(Ae^u+Be^(-u))=0.

delta(x-t)=sum_(n=0)^inftyphi_n(x)phi_n(t), where delta(x) is the delta function.

The continuous Fourier transform is defined as f(nu) = F_t[f(t)](nu) (1) = int_(-infty)^inftyf(t)e^(-2piinut)dt. (2) Now consider generalization to the case of a discrete ...

The second-order ordinary differential equation (x^2y^')^'+x^2y^n=0.

The field axioms are generally written in additive and multiplicative pairs. name addition multiplication associativity (a+b)+c=a+(b+c) (ab)c=a(bc) commutativity a+b=b+a ...