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Let {f_n(x)} be a sequence of analytic functions regular in a region G, and let this sequence be uniformly convergent in every closed subset of G. If the analytic function ...

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 ...

The statistical index P_H=(sumv_0)/(sum(v_0p_0)/(p_n))=(sump_0q_0)/(sum(p_0^2q_0)/(p_n)), where p_n is the price per unit in period n, q_n is the quantity produced in period ...

A circle surrounded by a square looks larger than the same circle surrounding a square.

Let f(z) be an analytic function in |z-a|<R. Then f(z)=1/(2pi)int_0^(2pi)f(z+re^(itheta))dtheta for 0<r<R.

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

The sum of the reciprocals of roots of an equation equals the negative coefficient of the linear term in the Maclaurin series.

A square number, also called a perfect square, is a figurate number of the form S_n=n^2, where n is an integer. The square numbers for n=0, 1, ... are 0, 1, 4, 9, 16, 25, 36, ...

The term perfect square is used to refer to a square number, a perfect square dissection, or a factorable quadratic polynomial of the form a^2+/-2ab+b^2=(a+/-b)^2.

A number which is simultaneously square and triangular. Let T_n denote the nth triangular number and S_m the mth square number, then a number which is both triangular and ...