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The most common "sine integral" is defined as Si(z)=int_0^z(sint)/tdt (1) Si(z) is the function implemented in the Wolfram Language as the function SinIntegral[z]. Si(z) is ...

The quasiperiodic function defined by d/(dz)lnsigma(z;g_2,g_3)=zeta(z;g_2,g_3), (1) where zeta(z;g_2,g_3) is the Weierstrass zeta function and lim_(z->0)(sigma(z))/z=1. (2) ...

If F is an algebraic Galois extension field of K such that the Galois group of the extension is Abelian, then F is said to be an Abelian extension of K. For example, ...

An element of an adèle group, sometimes called a repartition in older literature (e.g., Chevalley 1951, p. 25). Adèles arise in both number fields and function fields. The ...

The coordinates representing any point of an n-dimensional affine space A by an n-tuple of real numbers, thus establishing a one-to-one correspondence between A and R^n. If V ...

Let P be the set of prime ideals of a commutative ring A. Then an affine scheme is a technical mathematical object defined as the ring spectrum sigma(A) of P, regarded as a ...

The ampersand curve is the name given by Cundy and Rowlett (1989, p. 72) to the quartic curve with implicit equation (y^2-x^2)(x-1)(2x-3)=4(x^2+y^2-2x)^2. (1) Although it is ...

Let M^n be a compact n-dimensional oriented Riemannian manifold without boundary, let O be a group representation of pi_1(M) by orthogonal matrices, and let E(O) be the ...

A surface of revolution defined by Kepler. It consists of more than half of a circular arc rotated about an axis passing through the endpoints of the arc. The equations of ...

The bicorn, sometimes also called the "cocked hat curve" (Cundy and Rollett 1989, p. 72), is the name of a collection of quartic curves studied by Sylvester in 1864 and ...