WebThe Wolfram Language supports zeta and polylogarithm functions of a complex variable in full generality, performing efficient arbitrary-precision evaluation and implementing extensive symbolic transformations. Zeta — Riemann and generalized Riemann zeta function. RiemannSiegelZ RiemannSiegelTheta StieltjesGamma RiemannXi. WebThis function is defined in analogy with the Riemann zeta function as providing the sum of the alternating series. η ( s) = ∑ k = 0 ∞ ( − 1) k k s = 1 − 1 2 s + 1 3 s − 1 4 s + …. The eta …
The Computation of Polylogarithms - University of Kent
WebSome other important sources of information on polylogarithm functions are the works of References and . In References [ 5 ] and [ 6 ], the authors explore the algorithmic and analytic properties of generalized harmonic Euler sums systematically, in order to compute the massive Feynman integrals which arise in quantum field theories and in certain … WebIt appears that the only known representations for the Riemann zeta function ((z) in terms of continued fractions are those for z = 2 and 3. Here we give a rapidly converging continued-fraction expansion of ((n) for any integer n > 2. This is a special case of a more general expansion which we have derived for the polylogarithms of order n, n > 1, by using the … durham university silvercloud
Polylogarithm -- from Wolfram MathWorld
Weba refinement involving a “lifting” from R to C/(2πi)mQ of the mth polylogarithm function. The natural setting for all of this is algebraic K-theory and the conjectures about polylogarithms lead to a purely algebraic (conjectural) … In mathematics, Spence's function, or dilogarithm, denoted as Li2(z), is a particular case of the polylogarithm. Two related special functions are referred to as Spence's function, the dilogarithm itself: and its reflection. For z < 1, an infinite series also applies (the integral definition constitutes its analytical extension to the complex plane): WebIn mathematics, the complete Fermi–Dirac integral, named after Enrico Fermi and Paul Dirac, for an index j is defined by = (+) +, (>)This equals + (), where is the polylogarithm.. Its … durham university shared rooms