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Expressions of the form lim_(k->infty)x_0+sqrt(x_1+sqrt(x_2+sqrt(...+x_k))) (1) are called nested radicals. Herschfeld (1935) proved that a nested radical of real nonnegative ...

The (complete) gamma function Gamma(n) is defined to be an extension of the factorial to complex and real number arguments. It is related to the factorial by Gamma(n)=(n-1)!, ...

Any pair of equations giving the real part of a function as an integral of its imaginary part and the imaginary part as an integral of its real part. Dispersion relationships ...

A continuous real function L(x,y) defined on the tangent bundle T(M) of an n-dimensional smooth manifold M is said to be a Finsler metric if 1. L(x,y) is differentiable at ...

The regulator of a number field K is a positive number associated with K. The regulator of an imaginary quadratic field is 1 and that of a real quadratic, imaginary cubic, or ...

The second Mersenne prime M_3=2^3-1, which is itself the exponent of Mersenne prime M_7=2^7-1=127. It gives rise to the perfect number P_7=M_7·2^6=8128. It is a Gaussian ...

The quartic curve given by the implicit equation (x^2-a^2)(x-a)^2+(y^2-a^2)^2=0, (1) so-named because of its resemblance to a tooth. The bicuspid curve has cusps at (a,-a) ...

Calabi's triangle is the unique triangle other that the equilateral triangle for which the largest inscribed square can be inscribed in three different ways (Calabi 1997). ...

The chi distribution with n degrees of freedom is the distribution followed by the square root of a chi-squared random variable. For n=1, the chi distribution is a ...

A prime factorization algorithm which uses residues produced in the continued fraction of sqrt(mN) for some suitably chosen m to obtain a square number. The algorithm solves ...