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Let F be the Maclaurin series of a meromorphic function f with a finite or infinite number of poles at points z_k, indexed so that 0<|z_1|<=|z_2|<=|z_3|<=..., then a pole ...

A cylindric section is the intersection of a plane with a right circular cylinder. It is a circle (if the plane is at a right angle to the axis), an ellipse, or, if the plane ...

Darboux's formula is a theorem on the expansion of functions in infinite series and essentially consists of integration by parts on a specific integrand product of functions. ...

An fairly good numerical integration technique. The method is also available in the Wolfram Language using the option Method -> DoubleExponential to NIntegrate.

A variable that appears in a calculation only as a placeholder and which disappears completely in the final result. For example, in the integral int_0^xf(x^')dx^', x^' is a ...

Let E be an elliptic curve defined over the field of rationals Q(sqrt(-d)) having equation y^2=x^3+ax+b with a and b integers. Let P be a point on E with integer coordinates ...

A module M over a unit ring R is called faithful if for all distinct elements a, b of R, there exists x in M such that ax!=bx. In other words, the multiplications by a and by ...

In 1657, Fermat posed the problem of finding solutions to sigma(x^3)=y^2, and solutions to sigma(x^2)=y^3, where sigma(n) is the divisor function (Dickson 2005). The first ...

Let S be a nonempty set, then a filter on S is a nonempty collection F of subsets of S having the following properties: 1. emptyset not in F, 2. If A,B in F, then A ...

An extension field F subset= K is called finite if the dimension of K as a vector space over F (the so-called degree of K over F) is finite. A finite field extension is ...