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Unlike quadratic, cubic, and quartic polynomials, the general quintic cannot be solved algebraically in terms of a finite number of additions, subtractions, multiplications, ...

Let L be a finite-dimensional split semisimple Lie algebra over a field of field characteristic 0, H a splitting Cartan subalgebra, and Lambda a weight of H in a ...

Van der Corput's constant is given by m = 2sqrt(2)int_0^(sqrt(pi/2-c))cos(x^2+c)dx (1) = 2pi[coscC(phi)-sincS(phi)] (2) = 3.3643175781... (3) (OEIS A143305), where C(x) and ...

Recall the definition of the autocorrelation function C(t) of a function E(t), C(t)=int_(-infty)^inftyE^_(tau)E(t+tau)dtau. (1) Also recall that the Fourier transform of E(t) ...

The sawtooth wave, called the "castle rim function" by Trott (2004, p. 228), is the periodic function given by S(x)=Afrac(x/T+phi), (1) where frac(x) is the fractional part ...

The m+1 ellipsoidal harmonics when kappa_1, kappa_2, and kappa_3 are given can be arranged in such a way that the rth function has r-1 zeros between -a^2 and -b^2 and the ...

The Chebotarev density theorem is a complicated theorem in algebraic number theory which yields an asymptotic formula for the density of prime ideals of a number field K that ...

A root-finding method which was among the most popular methods for finding roots of univariate polynomials in the 19th and 20th centuries. It was invented independently by ...

The theta series of a lattice is the generating function for the number of vectors with norm n in the lattice. Theta series for a number of lattices are implemented in the ...

The following are equivalent definitions for a Galois extension field (also simply known as a Galois extension) K of F. 1. K is the splitting field for a collection of ...