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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 ...

int_0^z(t^mu)/(1+t)dt=z/(mu+1+((mu+1)^2z)/((mu+2)-(mu+1)z+((mu+2)^2z)/((mu+3)-(mu+2)z+...))) for mu>-1 and -1<z<=1 (Perron 1954-1957, p. 18; Borwein et al. 2004, p. 35).

D_P(x)=lim_(epsilon->0)(lnmu(B_epsilon(x)))/(lnepsilon), where B_epsilon(x) is an n-dimensional ball of radius epsilon centered at x and mu is the probability measure.

The l^infty-polynomial norm defined for a polynomial P=a_kx^k+...+a_1x+a_0 by ||P||_infty=max_(k)|a_k|. Note that some authors (especially in the area of Diophantine ...

Quasirandom numbers are numbers selected from a quasirandom sequence. Such numbers are useful in computational problems such as quasi-Monte Carlo integration.

Given a polynomial in a single complex variable with complex coefficients p(z)=a_nz^n+a_(n-1)z^(n-1)+...+a_0, the reciprocal polynomial is defined by ...

Let m and m+h be two consecutive critical indices of f and let F be (m+h)-normal. If the polynomials p^~_k^((n)) are defined by p^~_0^((n))(u) = 1 (1) p^~_(k+1)^((n))(u) = ...

A generalization of the Gaussian sum. For p and q of opposite parity (i.e., one is even and the other is odd), Schaar's identity states ...

Let a general theta function be defined as T(x,q)=sum_(n=-infty)^inftyx^nq^(n^2), then

An algorithm that can always be used to decide whether a given polynomial is free of zeros in the closed unit disk (or, using an entire linear transformation, to any other ...