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Given a Jacobi amplitude phi and a elliptic modulus m in an elliptic integral, Delta(phi)=sqrt(1-msin^2phi).

The associated Legendre polynomials P_l^m(x) and P_l^(-m)(x) generalize the Legendre polynomials P_l(x) and are solutions to the associated Legendre differential equation, ...

Given a field F and an extension field K superset= F, if alpha in K is an algebraic element over F, the minimal polynomial of alpha over F is the unique monic irreducible ...

The maximal matching-generating polynomial M_G(x) for the graph G may be defined as the polynomial M_G(x)=sum_(k=nu_L(G))^(nu(G))m_kx^k, where nu_L(G) is the lower matching ...

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 ...

Given a Jacobi amplitude phi in an elliptic integral, the argument u is defined by the relation phi=am(u,k). It is related to the elliptic integral of the first kind F(u,k) ...

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)). ...

The Legendre symbol is a number theoretic function (a/p) which is defined to be equal to +/-1 depending on whether a is a quadratic residue modulo p. The definition is ...

One of the quantities lambda_i appearing in the Gauss-Jacobi mechanical quadrature. They satisfy lambda_1+lambda_2+...+lambda_n = int_a^bdalpha(x) (1) = alpha(b)-alpha(a) (2) ...