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Let alpha_(n+1) = (2alpha_nbeta_n)/(alpha_n+beta_n) (1) beta_(n+1) = sqrt(alpha_nbeta_n), (2) then H(alpha_0,beta_0)=lim_(n->infty)a_n=1/(M(alpha_0^(-1),beta_0^(-1))), (3) ...

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 ...

The Greek problems of antiquity were a set of geometric problems whose solution was sought using only compass and straightedge: 1. circle squaring. 2. cube duplication. 3. ...

The statistical index P_G=[product((p_n)/(p_0))^(v_0)]^(1/Sigmav_0), where p_n is the price per unit in period n, q_n is the quantity produced in period n, and v_n=p_nq_n the ...

Given a planar graph G, its geometric dual G^* is constructed by placing a vertex in each region of G (including the exterior region) and, if two regions have an edge x in ...

A hypergeometric series sum_(k)c_k is a series for which c_0=1 and the ratio of consecutive terms is a rational function of the summation index k, i.e., one for which ...

Let E be a compact connected subset of d-dimensional Euclidean space. Gross (1964) and Stadje (1981) proved that there is a unique real number a(E) such that for all x_1, ...

An arithmetic series is the sum of a sequence {a_k}, k=1, 2, ..., in which each term is computed from the previous one by adding (or subtracting) a constant d. Therefore, for ...

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.