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Given a elliptic modulus k in an elliptic integral, the modular angle alpha is defined by k=sinalpha. An elliptic integral is written I(phi|m) when the parameter m is used, ...

The Dedekind eta function is defined over the upper half-plane H={tau:I[tau]>0} by eta(tau) = q^_^(1/24)(q^_)_infty (1) = q^_^(1/24)product_(k=1)^(infty)(1-q^_^k) (2) = ...

A prime factorization algorithm also known as Pollard Monte Carlo factorization method. There are two aspects to the Pollard rho factorization method. The first is the idea ...

A primality test is a test to determine whether or not a given number is prime, as opposed to actually decomposing the number into its constituent prime factors (which is ...

The variable phi (also denoted am(u,k)) used in elliptic functions and elliptic integrals is called the amplitude (or Jacobi amplitude). It can be defined by phi = am(u,k) ...

The notion of an inverse is used for many types of mathematical constructions. For example, if f:T->S is a function restricted to a domain S and range T in which it is ...

The curve produced by fixed point P on the circumference of a small circle of radius b rolling around the inside of a large circle of radius a>b. A hypocycloid is therefore a ...

A wide variety of large numbers crop up in mathematics. Some are contrived, but some actually arise in proofs. Often, it is possible to prove existence theorems by deriving ...

A linear transformation between two vector spaces V and W is a map T:V->W such that the following hold: 1. T(v_1+v_2)=T(v_1)+T(v_2) for any vectors v_1 and v_2 in V, and 2. ...

Mills' constant can be defined as the least theta such that f_n=|_theta^(3^n)_| is prime for all positive integers n (Caldwell and Cheng 2005). The first few f_n for n=1, 2, ...