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Let omega be the cube root of unity (-1+isqrt(3))/2. Then the Eisenstein primes are Eisenstein integers, i.e., numbers of the form a+bomega for a and b integers, such that ...

Eisenstein's irreducibility criterion is a sufficient condition assuring that an integer polynomial p(x) is irreducible in the polynomial ring Q[x]. The polynomial ...

A graph G with m edges is said to be elegant if the vertices of G can be labeled with distinct integers (0,1,2,...,m) in such a way that the set of values on the edges ...

A fact noticed by physicist G. Gamow when he had an office on the second floor and physicist M. Stern had an office on the sixth floor of a seven-story building (Gamow and ...

The first solution to Lamé's differential equation, denoted E_n^m(x) for m=1, ..., 2n+1. They are also called Lamé functions. The product of two ellipsoidal harmonics of the ...

Ellipsoidal harmonics of the second kind, also known as Lamé functions of the second kind, are variously defined as F_m^p(x)=(2m+1)E_m^p(x) ...

The ordinary differential equation y^('')-(a+bk^2sn^2x+qk^4sn^4x)y=0, where snx=sn(x,k) is a Jacobi elliptic function (Arscott 1981).

Elliptic alpha functions relate the complete elliptic integrals of the first K(k_r) and second kinds E(k_r) at elliptic integral singular values k_r according to alpha(r) = ...

The group of an elliptic curve which has been transformed to the form y^2=x^3+ax+b is the set of K-rational points, including the single point at infinity. The group law ...

The elliptic exponential function eexp_(a,b)(u) gives the value of x in the elliptic logarithm eln_(a,b)(x)=1/2int_infty^x(dt)/(sqrt(t^3+at^2+bt)) for a and b real such that ...