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The polynomials M_k(x;delta,eta) which form the Sheffer sequence for g(t) = {[1+deltaf(t)]^2+[f(t)]^2}^(eta/2) (1) f(t) = tan(t/(1+deltat)) (2) which have generating function ...

(1) where H_n(x) is a Hermite polynomial (Watson 1933; Erdélyi 1938; Szegö 1975, p. 380). The generating function ...

Polynomials b_n(x) which form a Sheffer sequence with g(t) = t/(e^t-1) (1) f(t) = e^t-1, (2) giving generating function sum_(k=0)^infty(b_k(x))/(k!)t^k=(t(t+1)^x)/(ln(1+t)). ...

A modified set of Chebyshev polynomials defined by a slightly different generating function. They arise in the development of four-dimensional spherical harmonics in angular ...

The root separation (or zero separation) of a polynomial P(x) with roots r_1, r_2, ... is defined by Delta(P)=min_(i!=j)|r_i-r_j|. There are lower bounds on how close two ...

A quantity such as a polynomial discriminant which remains unchanged under a given class of algebraic transformations. Such invariants were originally called ...

Given the binary quadratic form ax^2+2bxy+cy^2 (1) with polynomial discriminant b^2-ac, let x = pX+qY (2) y = rX+sY. (3) Then a(pX+qY)^2+2b(pX+qY)(rX+sY)+c(rX+sY)^2 ...

Let O be an order of an imaginary quadratic field. The class equation of O is the equation H_O=0, where H_O is the extension field minimal polynomial of j(O) over Q, with ...

The AC method is an algorithm for factoring quadratic polynomials of the form p(x)=Ax^2+Bx+C with integer coefficients. As its name suggests, the crux of the algorithm is to ...

Two elements alpha, beta of a field K, which is an extension field of a field F, are called conjugate (over F) if they are both algebraic over F and have the same minimal ...