WebMar 24, 2024 · The function reduces to the usual polylogarithm for the case S_(n-1,1)(z)=Li_n(z). The Nielsen generalized polylogarithm is implemented as PolyLog[n, p, z]. TOPICS In mathematics, the polylogarithm (also known as Jonquière's function, for Alfred Jonquière) is a special function Lis(z) of order s and argument z. Only for special values of s does the polylogarithm reduce to an elementary function such as the natural logarithm or a rational function. In quantum statistics, the … See more In the case where the order $${\displaystyle s}$$ is an integer, it will be represented by $${\displaystyle s=n}$$ (or $${\displaystyle s=-n}$$ when negative). It is often convenient to define Depending on the … See more • For z = 1, the polylogarithm reduces to the Riemann zeta function Li s ⁡ ( 1 ) = ζ ( s ) ( Re ⁡ ( s ) > 1 ) . {\displaystyle \operatorname {Li} … See more 1. As noted under integral representations above, the Bose–Einstein integral representation of the polylogarithm may be extended to … See more The dilogarithm is the polylogarithm of order s = 2. An alternate integral expression of the dilogarithm for arbitrary complex argument z is (Abramowitz & Stegun 1972, § 27.7): A source of confusion is that some computer algebra systems See more For particular cases, the polylogarithm may be expressed in terms of other functions (see below). Particular values for the … See more Any of the following integral representations furnishes the analytic continuation of the polylogarithm beyond the circle of … See more For z ≫ 1, the polylogarithm can be expanded into asymptotic series in terms of ln(−z): where B2k are the Bernoulli numbers. Both versions hold for all … See more

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Webdict.cc German-English Dictionary: Translation for legale Funktion WebThe polylogarithm Li_n(z), also known as the Jonquière's function, is the function Li_n(z)=sum_(k=1)^infty(z^k)/(k^n) (1) defined in the complex plane over the open unit … foam camo trucker hat

Polylogarithm - MATLAB polylog - MathWorks Deutschland

WebFeb 9, 2024 · The dilogarithm function. Li2(x) =: ∞ ∑ n=1 xn n2, Li 2 ( x) =: ∑ n = 1 ∞ x n n 2, (1) studied already by Leibniz, is a special case of the polylogarithm function. Lis(x) =: ∞ … Webgives the Nielsen generalized polylogarithm function . Details. Mathematical function, suitable for both symbolic and numerical manipulation.. . . PolyLog [n, z] has a branch cut … WebThe logarithmic integral function (the integral logarithm) uses the same notation, li(x), but without an index. The toolbox provides the logint function to compute the logarithmic integral function. Floating-point evaluation of … foam camp bed