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The Dirichlet beta function is defined by the sum beta(x) = sum_(n=0)^(infty)(-1)^n(2n+1)^(-x) (1) = 2^(-x)Phi(-1,x,1/2), (2) where Phi(z,s,a) is the Lerch transcendent. The ...

A discrete group is a topological group with the discrete topology. Often in practice, discrete groups arise as discrete subgroups of continuous Lie groups acting on a ...

A dissection fallacy is an apparent paradox arising when two plane figures with different areas seem to be composed by the same finite set of parts. In order to produce this ...

The distance between two points is the length of the path connecting them. In the plane, the distance between points (x_1,y_1) and (x_2,y_2) is given by the Pythagorean ...

A double bubble is pair of bubbles which intersect and are separated by a membrane bounded by the intersection. The usual double bubble is illustrated in the left figure ...

A function f(z) is said to be doubly periodic if it has two periods omega_1 and omega_2 whose ratio omega_2/omega_1 is not real. A doubly periodic function that is analytic ...

A doubly periodic function with periods 2omega_1 and 2omega_2 such that f(z+2omega_1)=f(z+2omega_2)=f(z), (1) which is analytic and has no singularities except for poles in ...

The elliptic lambda function lambda(tau) is a lambda-modular function defined on the upper half-plane by lambda(tau)=(theta_2^4(0,q))/(theta_3^4(0,q)), (1) where tau is the ...

A surface of revolution which is generalization of the ring torus. It is produced by rotating an ellipse having horizontal semi-axis a, vertical semi-axis b, embedded in the ...

An elongated square pyramid is a solid formed by attaching a square pyramid atop a square prism. Such a solid might also be termed an obelisk (although that term is also used ...