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If k is the elliptic modulus of an elliptic integral or elliptic function, then k^'=sqrt(1-k^2) (1) is called the complementary modulus. Complete elliptic integrals with ...

If g(theta) is a trigonometric polynomial of degree m satisfying the condition |g(theta)|<=1 where theta is arbitrary and real, then g^'(theta)<=m.

The number theta in the quadric (x^2)/(a^2+theta)+(y^2)/(b^2+theta)+(z^2)/(c^2+theta)=1 is called the parameter.

A quantity which does not exhibit estimator bias. An estimator theta^^ is an unbiased estimator of theta if <theta^^>=theta.

Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let phi(n) or phi(x) be a positive function and f(n) or ...

The Lerch transcendent is generalization of the Hurwitz zeta function and polylogarithm function. Many sums of reciprocal powers can be expressed in terms of it. It is ...

Let M(X) denote the group of all invertible maps X->X and let G be any group. A homomorphism theta:G->M(X) is called an action of G on X. Therefore, theta satisfies 1. For ...

A product involving an infinite number of terms. Such products can converge. In fact, for positive a_n, the product product_(n=1)^(infty)a_n converges to a nonzero number iff ...

tau is the ratio tau=omega_2/omega_1 of the two half-periods omega_1 and omega_2 of an elliptic function (Whittaker and Watson 1990, pp. 463 and 473) defined such that the ...

The symbol O(x), pronounced "big-O of x," is one of the Landau symbols and is used to symbolically express the asymptotic behavior of a given function. In particular, if n is ...