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The arithmetic-geometric energy of a graph is defined as the graph energy of its arithmetic-geometric matrix, i.e., the sum of the absolute values of the eigenvalues of its ...

Let a_(n+1) = 1/2(a_n+b_n) (1) b_(n+1) = (2a_nb_n)/(a_n+b_n). (2) Then A(a_0,b_0)=lim_(n->infty)a_n=lim_(n->infty)b_n=sqrt(a_0b_0), (3) which is just the geometric mean.

The fundamental theorem of arithmetic states that every positive integer (except the number 1) can be represented in exactly one way apart from rearrangement as a product of ...

An arithmetic progression of primes is a set of primes of the form p_1+kd for fixed p_1 and d and consecutive k, i.e., {p_1,p_1+d,p_1+2d,...}. For example, 199, 409, 619, ...

Simply stated, floating-point arithmetic is arithmetic performed on floating-point representations by any number of automated devices. Traditionally, this definition is ...

The arithmetic-geometric mean agm(a,b) of two numbers a and b (often also written AGM(a,b) or M(a,b)) is defined by starting with a_0=a and b_0=b, then iterating a_(n+1) = ...

Almost all natural numbers are very, very, very large (Steinbach 1990, p. 111).

By way of analogy with the prime counting function pi(x), the notation pi_(a,b)(x) denotes the number of primes of the form ak+b less than or equal to x (Shanks 1993, pp. ...

For positive numbers a and b with a!=b, (a+b)/2>(b-a)/(lnb-lna)>sqrt(ab).

The arithmetic-geometric spectral radius rho_(AG) of a graph is defined as the largest eigenvalue of its arithmetic-geometric matrix.