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product_(k=1)^(infty)(1-x^k) = sum_(k=-infty)^(infty)(-1)^kx^(k(3k+1)/2) (1) = 1+sum_(k=1)^(infty)(-1)^k[x^(k(3k-1)/2)+x^(k(3k+1)/2)] (2) = (x)_infty (3) = ...

Every nonconstant entire function attains every complex value with at most one exception (Henrici 1988, p. 216; Apostol 1997). Furthermore, every analytic function assumes ...

A pyramidal frustum is a frustum made by chopping the top off a pyramid. It is a special case of a prismatoid. For a right pyramidal frustum, let s be the slant height, h the ...

A sequence of n-tuples that fills n-space more uniformly than uncorrelated random points, sometimes also called a low-discrepancy sequence. Although the ordinary uniform ...

A closed planar quadrilateral with opposite sides of equal lengths a and b, and with four right angles. A square is a degenerate rectangle with a=b. The area of the rectangle ...

A process of successively crossing out members of a list according to a set of rules such that only some remain. The best known sieve is the sieve of Eratosthenes for ...

A Smarandache-Wellin number that is prime is known as a Smarandache-Wellin prime. Concatenations of the first n=1, 2, 4, 128, 174, 342, 435, 1429 (OEIS A046035; Ibstedt 1998, ...

That portion of geometry dealing with solids, as opposed to plane geometry. Solid geometry is concerned with polyhedra, spheres, three-dimensional solids, lines in ...

A solid of revolution is a solid enclosing the surface of revolution obtained by rotating a 1-dimensional curve, line, etc. about an axis. A portion of a solid of revolution ...

A spherical cap is the region of a sphere which lies above (or below) a given plane. If the plane passes through the center of the sphere, the cap is a called a hemisphere, ...