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For a subgroup H of a group G, the index of H, denoted (G:H), is the cardinal number of the set of left cosets of H in G (which is equal to the cardinal number of the set of ...

An element of an extension field of a field F which is not algebraic over F. A transcendental number is a complex number which is transcendental over the field Q of rational ...

A number n which is an integer multiple k of the sum of its unitary divisors sigma^*(n) is called a unitary k-multiperfect number. There are no odd unitary multiperfect ...

The upper domination number Gamma(G) of a graph G is the maximum size of a minimal dominating set of vertices in G. The (lower) domination number may be similarly defined as ...

How far can a stack of n books protrude over the edge of a table without the stack falling over? It turns out that the maximum overhang possible d_n for n books (in terms of ...

Champernowne's constant C=0.12345678910111213... (1) (OEIS A033307) is the number obtained by concatenating the positive integers and interpreting them as decimal digits to ...

A number of closed-form constants can be obtained for generalized continued fractions having particularly simple partial numerators and denominators. The Ramanujan continued ...

The Delannoy numbers D(a,b) are the number of lattice paths from (0,0) to (b,a) in which only east (1, 0), north (0, 1), and northeast (1, 1) steps are allowed (i.e., ->, ^, ...

The natural logarithm lnx is the logarithm having base e, where e=2.718281828.... (1) This function can be defined lnx=int_1^x(dt)/t (2) for x>0. This definition means that e ...

Q(n), also denoted q(n) (Abramowitz and Stegun 1972, p. 825), gives the number of ways of writing the integer n as a sum of positive integers without regard to order with the ...