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Voronin (1975) proved the remarkable analytical property of the Riemann zeta function zeta(s) that, roughly speaking, any nonvanishing analytic function can be approximated ...

Skewness is a measure of the degree of asymmetry of a distribution. If the left tail (tail at small end of the distribution) is more pronounced than the right tail (tail at ...

The mean deviation (also called the mean absolute deviation) is the mean of the absolute deviations of a set of data about the data's mean. For a sample size N, the mean ...

The "kurtosis excess" (Kenney and Keeping 1951, p. 27) is defined in terms of the usual kurtosis by gamma_2 = beta_2-3 (1) = (mu_4)/(mu_2^2)-3. (2) It is commonly denoted ...

The polylogarithm Li_n(z), also known as the Jonquière's function, is the function Li_n(z)=sum_(k=1)^infty(z^k)/(k^n) (1) defined in the complex plane over the open unit ...

The prime number theorem gives an asymptotic form for the prime counting function pi(n), which counts the number of primes less than some integer n. Legendre (1808) suggested ...

The probability density function (PDF) P(x) of a continuous distribution is defined as the derivative of the (cumulative) distribution function D(x), D^'(x) = ...

Count the number of lattice points N(r) inside the boundary of a circle of radius r with center at the origin. The exact solution is given by the sum N(r) = ...

A correction to a discrete binomial distribution to approximate a continuous distribution. P(a<=X<=b) approx P((a-1/2-np)/(sqrt(np(1-p)))<=z<=(b+1/2-np)/(sqrt(np(1-p)))), ...

Let T_n(x) be an arbitrary trigonometric polynomial T_n(x)=1/2a_0+{sum_(k=1)^n[a_kcos(kx)+b_ksin(kx)]} (1) with real coefficients, let f be a function that is integrable over ...