Search Results for ""

Polynomials s_n(x) which form the Sheffer sequence for f^(-1)(t)=1+t-e^t, (1) where f^(-1)(t) is the inverse function of f(t), and have generating function ...

For a polynomial P(x_1,x_2,...,x_k), the Mahler measure of P is defined by (1) Using Jensen's formula, it can be shown that for P(x)=aproduct_(i=1)^(n)(x-alpha_i), ...

A polynomial is a mathematical expression involving a sum of powers in one or more variables multiplied by coefficients. A polynomial in one variable (i.e., a univariate ...

An unsolved problem in mathematics attributed to Lehmer (1933) that concerns the minimum Mahler measure M_1(P) for a univariate polynomial P(x) that is not a product of ...

Let K be a field of field characteristic 0 (e.g., the rationals Q) and let {u_n} be a sequence of elements of K which satisfies a difference equation of the form ...

If {a_0,a_1,...} is a recursive sequence, then the set of all k such that a_k=0 is the union of a finite (possibly empty) set and a finite number (possibly zero) of full ...

A Z-number is a real number xi such that 0<=frac[(3/2)^kxi]<1/2 for all k=1, 2, ..., where frac(x) is the fractional part of x. Mahler (1968) showed that there is at most one ...

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 ...

The Lehmer-Mahler is the following integral representation for the Legendre polynomial P_n(x): P_n(costheta) = 1/piint_0^pi(costheta+isinthetacosphi)^ndphi (1) = ...

A knot invariant in the form of a polynomial such as the Alexander polynomial, BLM/Ho Polynomial, bracket polynomial, Conway polynomial, HOMFLY polynomial, Jones polynomial, ...