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The second solution Q_l(x) to the Legendre differential equation. The Legendre functions of the second kind satisfy the same recurrence relation as the Legendre polynomials. ...

A proof that is only based on visual elements, without any comments. An arithmetic identity can be demonstrated by a picture showing a self-evident equality between numerical ...

There are a number of functions in various branches of mathematics known as Riemann functions. Examples include the Riemann P-series, Riemann-Siegel functions, Riemann theta ...

A map projection obtained by projecting points P on the surface of sphere from the sphere's north pole N to point P^' in a plane tangent to the south pole S (Coxeter 1969, p. ...

A double integral over three coordinates giving the area within some region R, A=intint_(R)dxdy. If a plane curve is given by y=f(x), then the area between the curve and the ...

The sextic curve also known as atriphtothlassic curve and given by the equation x^4(x^2+y^2)-(ax^2-b)^2=0, where a,b>0.

The number of coincidences of a (nu,nu^') correspondence of value gamma on a curve of curve genus p is given by nu+nu^'+2pgamma.

A mathematical structure A is said to be closed under an operation + if, whenever a and b are both elements of A, then so is a+b. A mathematical object taken together with ...

In 1976, Coates and Wiles showed that elliptic curves with complex multiplication having an infinite number of solutions have L-functions which are zero at the relevant fixed ...

A cusp is a point at which two branches of a curve meet such that the tangents of each branch are equal. The above plot shows the semicubical parabola curve x^3-y^2=0, which ...