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A number t_x=tan^(-1)(1/x)=cot^(-1)x, where x is an integer or rational number, tan^(-1)x is the inverse tangent, and cot^(-1)x is the inverse cotangent. Gregory numbers ...

The Machin-like formula 1/4pi=2cot^(-1)(2)-cot^(-1)(7). The other 2-term Machin-like formulas are Euler's Machin-like formula, Hutton's formula, and Machin's formula.

The Machin-like formula 1/4pi=2cot^(-1)(3)+cot^(-1)(7). The other two-term Machin-like formulas are Euler's Machin-like formula, Hermann's formula, and Machin's formula.

Let S(x) denote the number of positive integers not exceeding x which can be expressed as a sum of two squares (i.e., those n<=x such that the sum of squares function ...

For a sequence {chi_i}, the Levine-O'Sullivan greedy algorithm is given by chi_1 = 1 (1) chi_i = max_(1<=j<=i-1)(j+1)(i-chi_j) (2) for i>1. The sequence generated by this ...

The natural logarithm of 2 is a transcendental quantity that arises often in decay problems, especially when half-lives are being converted to decay constants. ln2 has ...

An orthogonal basis of vectors is a set of vectors {x_j} that satisfy x_jx_k=C_(jk)delta_(jk) and x^mux_nu=C_nu^mudelta_nu^mu, where C_(jk), C_nu^mu are constants (not ...

The Machin-like formula 1/4pi=cot^(-1)2+cot^(-1)5+cot^(-1)8.

Given a nonhomogeneous ordinary differential equation, select a differential operator which will annihilate the right side, and apply it to both sides. Find the solution to ...

Given an n-ball B^n of radius R, find the distribution of the lengths s of the lines determined by two points chosen at random within the ball. The probability distribution ...