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The orthogonal polynomials defined by c_n^((mu))(x) = _2F_0(-n,-x;;-mu^(-1)) (1) = ((-1)^n)/(mu^n)(x-n+1)_n_1F_1(-n;x-n+1;mu), (2) where (x)_n is the Pochhammer symbol ...

Let i_k(G) be the number of irredundant sets of size k in a graph G, then the irredundance polynomial R_G(x) of G in the variable x is defined as ...

The Lommel polynomials R_(m,nu)(z) arise from the equation J_(m+nu)(z)=J_nu(z)R_(m,nu)(z)-J_(nu-1)(z)R_(m-1,nu+1)(z), (1) where J_nu(z) is a Bessel function of the first kind ...

Polynomials s_k(x;a) which form the Sheffer sequence for g(t) = ((e^t-1)/t)^(-a) (1) f(t) = e^t-1 (2) which have generating function ...

Polynomials S_k(x) which form the Sheffer sequence for g(t) = e^(-t) (1) f^(-1)(t) = ln(1/(1-e^(-t))), (2) where f^(-1)(t) is the inverse function of f(t), and have ...

Let d_G(k) be the number of dominating sets of size k in a graph G, then the domination polynomial D_G(x) of G in the variable x is defined as ...

The polynomials defined by B_(i,n)(t)=(n; i)t^i(1-t)^(n-i), (1) where (n; k) is a binomial coefficient. The Bernstein polynomials of degree n form a basis for the power ...

The Zernike polynomials are a set of orthogonal polynomials that arise in the expansion of a wavefront function for optical systems with circular pupils. The odd and even ...

Adomian polynomials decompose a function u(x,t) into a sum of components u(x,t)=sum_(n=0)^inftyu_n(x,t) (1) for a nonlinear operator F as F(u(x,t))=sum_(n=0)^inftyA_n. (2) ...

The polynomials G_n(x;a,b) given by the associated Sheffer sequence with f(t)=e^(at)(e^(bt)-1), (1) where b!=0. The inverse function (and therefore generating function) ...