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An automorphic function f(z) of a complex variable z is one which is analytic (except for poles) in a domain D and which is invariant under a countably infinite group of ...

The bifolium is a folium with b=0. The bifolium is a quartic curve and is given by the implicit equation is (x^2+y^2)^2=4axy^2 (1) and the polar equation ...

The Brent-Salamin formula, also called the Gauss-Salamin formula or Salamin formula, is a formula that uses the arithmetic-geometric mean to compute pi. It has quadratic ...

Consider two cylinders as illustrated above (Hubbell 1965) where the cylinders have radii r_1 and r_2 with r_1<=r_2, the larger cylinder is oriented along the z-axis, and ...

The arithmetic-geometric mean agm(a,b) of two numbers a and b (often also written AGM(a,b) or M(a,b)) is defined by starting with a_0=a and b_0=b, then iterating a_(n+1) = ...

Let lambda_(m,n) be Chebyshev constants. Schönhage (1973) proved that lim_(n->infty)(lambda_(0,n))^(1/n)=1/3. (1) It was conjectured that the number ...

When a prime l divides the elliptic discriminant of a elliptic curve E, two or all three roots of E become congruent (mod l). An elliptic curve is semistable if, for all such ...

The function K(alpha,t) in an integral or integral transform g(alpha)=int_a^bf(t)K(alpha,t)dt. Whittaker and Robinson (1967, p. 376) use the term nucleus for kernel.

The quantity being integrated, also called the integral kernel. For example, in intf(x)dx, f(x) is the integrand.

A triple integral is a three-fold multiple integral of the form intintintf(x,y,z)dxdydz. Triple integrals arise in evaluating quantities such as the mass, volume, moment, ...