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Orthogonal polynomials are classes of polynomials {p_n(x)} defined over a range [a,b] that obey an orthogonality relation int_a^bw(x)p_m(x)p_n(x)dx=delta_(mn)c_n, (1) where ...

A symmetric polynomial on n variables x_1, ..., x_n (also called a totally symmetric polynomial) is a function that is unchanged by any permutation of its variables. In other ...

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 Alexander polynomial is a knot invariant discovered in 1923 by J. W. Alexander (Alexander 1928). The Alexander polynomial remained the only known knot polynomial until ...

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 ...

A multidimensional polylogarithm is a generalization of the usual polylogarithm to L_(a_1,...,a_m)(z)=sum_(n_1>...>n_m>0)(z^(n_1))/(n_1^(a_1)...n_m^(a_m)) with positive ...

A moment mu_n of a univariate probability density function P(x) taken about the mean mu=mu_1^', mu_n = <(x-<x>)^n> (1) = int(x-mu)^nP(x)dx, (2) where <X> denotes the ...

A moment mu_n of a probability function P(x) taken about 0, mu_n^' = <x^n> (1) = intx^nP(x)dx. (2) The raw moments mu_n^' (sometimes also called "crude moments") can be ...

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) = ...