Lattice sum and polylogarithm function
http://www.acta.sapientia.ro/acta-math/C10-2/math102-11.pdf WebCalculates the Polylogarithm function ${Li}_s(z)$ defined by ${Li}_s = \sum_{n=1}^{\infty} \frac{z^n}{n^s}$ Uses double precision complex numbers (not arbitrary precision).
Lattice sum and polylogarithm function
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Web11 jun. 2024 · In this paper, we explore the representation and many connections between integrals of products of polylogarithmic functions with alternating signs in the argument … WebThere's a GPL'd C library, ANANT - Algorithms in Analytic Number Theory by Linas Vepstas, which includes multiprecision implementation of the polylogarithm, building on GMP. From its README file: This project contains ad-hoc implementations of assorted analytic functions of interest in number theory, including the gamma function, the Riemann zeta …
WebThe Polylogarithm is also known as Jonquiere's function. It is defined as ∑ k = 1 ∞ z k / k n = z + z 2 / 2 n +... The polylogarithm function arises, e.g., in Feynman diagram … WebIn what follows, a function depending on the parameter and de ned by the Dirichlet power series Li = X1 k=1 zk k (1) is referred to as a polylogarithm. The series in (1) converges absolutely for all if jzj < 1forRe >0ifjzj=1andz6=1,andforRe >1ifz=1.Itisknownthat the polylogarithm can be extended to the whole −plane by means of a contour
Web3.2 Lattice sums and elliptic functions 128 3.3 A phase-modulated lattice sum 131 3.4 Double sums involving Bessel functions 134 3.5 Distributive lattice sums 140 3.6 … Web24 mrt. 2024 · Lattice Sum. where the prime indicates that the origin , , etc. is excluded from the sum (Borwein and Borwein 1986, p. 288). for , where is the Dirichlet beta function, is …
WebMathematical function, suitable for both symbolic and numerical manipulation. PolyLog [ n , z ] has a branch cut discontinuity in the complex plane running from 1 to . For certain …
WebThe notation logkn is often used as a shorthand for (log n)k, analogous to sin2θ for (sin θ)2 . In computer science, polylogarithmic functions occur as the order of time or memory used by some algorithms (e.g., "it has polylogarithmic order"), such as … two day town 2022Webler sums of the form X∞ n=1 HnH (m) n np (m+p≤ 8), and some integrals of polylogarithm functions of the form Z 1 0 Lir(x)Lip(x)Liq(x) x dx (r+p+q≤ 8) can be written in terms of Riemann zeta values. It is interesting that inte-grals of polylogarithm functions can be related to multiple zeta (star) values. talisman crossword clue the sunWeb197 Functional equations of polylogarithms Herbert Gangl 0. Introduction The polylogarithm functions (for short “polylogarithms”), defined by the power seri es talisman crossword clue dan wordWebThe polylogarithm function, Li p(z), is defined, and a number of algorithms are derived for its computation, valid in different ranges of its real parameter p and complex argument z. … talisman crossbowsWebIn mathematics, the Incomplete Polylogarithm function is related to the polylogarithm function. It is sometimes known as the incomplete Fermi–Dirac integral or the incomplete Bose–Einstein integral. It may be defined by: Expanding about z=0 and integrating gives a series representation: two day townWebПолилогарифм — специальная функция, обозначаемая и определяемая как бесконечный степенной ряд = =, где s и z — комплексные числа, причём … two day tour to petra from israelWebfor lattice scattering in a non-polar material and a polar material, 0r = and 1/2, respectively; for ionized impurity scattering r = 2 [22]. When the chemical potential becomes complex, … two day ticket to disney world