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A primitive polynomial is a polynomial that generates all elements of an extension field from a base field. Primitive polynomials are also irreducible polynomials. For any ...

A Lucas polynomial sequence is a pair of generalized polynomials which generalize the Lucas sequence to polynomials is given by W_n^k(x) = ...

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 ...

The approximating polynomial which has the smallest maximum deviation from the true function. It is closely approximated by the Chebyshev polynomials of the first kind.

Polynomials s_k(x) which form the Sheffer sequence for f(t)=-(2t)/(1-t^2) (1) and have exponential generating function ...

The polynomial giving the number of colorings with m colors of a structure defined by a permutation group.

The power polynomials x^n are an associated Sheffer sequence with f(t)=t, (1) giving generating function sum_(k=0)^inftyx^kt^k=1/(1-tx) (2) and exponential generating ...

A polynomial with coefficients in a field is separable if its factors have distinct roots in some extension field.

The distance polynomial is the characteristic polynomial of the graph distance matrix. The following table summarizes distance polynomials for some common classes of graphs. ...

The Euler polynomial E_n(x) is given by the Appell sequence with g(t)=1/2(e^t+1), (1) giving the generating function (2e^(xt))/(e^t+1)=sum_(n=0)^inftyE_n(x)(t^n)/(n!). (2) ...