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F(x) = -Li_2(-x) (1) = int_0^x(ln(1+t))/tdt, (2) where Li_2(x) is the dilogarithm.

The lemniscate functions arise in rectifying the arc length of the lemniscate. The lemniscate functions were first studied by Jakob Bernoulli and Giulio Fagnano. A historical ...

An alternative name for an associated Legendre polynomial.

The 34 distinct convergent hypergeometric series of order two enumerated by Horn (1931) and corrected by Borngässer (1933). There are 14 complete series for which ...

Toroidal functions are a class of functions also called ring functions that appear in systems having toroidal symmetry. Toroidal functions can be expressed in terms of the ...

P(n), sometimes also denoted p(n) (Abramowitz and Stegun 1972, p. 825; Comtet 1974, p. 94; Hardy and Wright 1979, p. 273; Conway and Guy 1996, p. 94; Andrews 1998, p. 1), ...

The computer animation format MPEG-7 uses Gabor functions to specify texture descriptors.

The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is ...

Let G be a group having normal subgroups H and K with H subset= K. Then K/H⊴G/H and (G/H)/(K/H)=G/K, where N⊴G indicates that N is a normal subgroup of G and G=H indicates ...

Affine functions represent vector-valued functions of the form f(x_1,...,x_n)=A_1x_1+...+A_nx_n+b. The coefficients can be scalars or dense or sparse matrices. The constant ...