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Hardy and Littlewood (1914) proved that the sequence {frac(x^n)}, where frac(x) is the fractional part, is equidistributed for almost all real numbers x>1 (i.e., the ...

The roots (sometimes also called "zeros") of an equation f(x)=0 are the values of x for which the equation is satisfied. Roots x which belong to certain sets are usually ...

The triakis icosahedral graph is Archimedean dual graph which is the skeleton of the triakis icosahedron. It is implemented in the Wolfram Language as ...

The triakis tetrahedral graph is Archimedean dual graph which is the skeleton of the triakis tetrahedron. It is implemented in the Wolfram Language as ...

Two lattice points (x,y) and (x^',y^') are mutually visible if the line segment joining them contains no further lattice points. This corresponds to the requirement that ...

A connective in logic known as the "exclusive or," or exclusive disjunction. It yields true if exactly one (but not both) of two conditions is true. The XOR operation does ...

Riemann defined the function f(x) by f(x) = sum_(p^(nu)<=x; p prime)1/nu (1) = sum_(n=1)^(|_lgx_|)(pi(x^(1/n)))/n (2) = pi(x)+1/2pi(x^(1/2))+1/3pi(x^(1/3))+... (3) (Hardy ...

The Weierstrass elliptic functions (or Weierstrass P-functions, voiced "p-functions") are elliptic functions which, unlike the Jacobi elliptic functions, have a second-order ...

The class of all regular sequences of particularly well-behaved functions equivalent to a given regular sequence. A distribution is sometimes also called a "generalized ...

A polygonal number is a type of figurate number that is a generalization of triangular, square, etc., to an n-gon for n an arbitrary positive integer. The above diagrams ...