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The modular group Gamma is the set of all transformations w of the form w(t)=(at+b)/(ct+d), where a, b, c, and d are integers and ad-bc=1. A Gamma-modular function is then ...

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 ...

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 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 ...

An apodization function similar to the Bartlett function.

Whittaker and Watson (1990, pp. 539-540) write Lamé's differential equation for ellipsoidal harmonics of the first kind of the four types as ...

where _2F_1(a,b;c;z) is a hypergeometric function and _3F_2(a,b,c;d,e;z) is a generalized hypergeometric function.

An elliptic integral is an integral of the form int(A(x)+B(x)sqrt(S(x)))/(C(x)+D(x)sqrt(S(x)))dx, (1) or int(A(x)dx)/(B(x)sqrt(S(x))), (2) where A(x), B(x), C(x), and D(x) ...