Polylogarithm function li
WebThis paper extends tools developed by Crandall (2012) 16 to provide robust, high-precision methods for computation of the incomplete Gamma function and the Lerch transcendent. We then apply these to the corresponding computation of the Hurwitz zeta ... WebMar 18, 2015 · The Γ derivative can be rewritten using that as Γ ′ ( z) = Γ ( z) ψ ( z), where ψ is the polygamma function of zeroth order. At the wanted situation, L i 0 ′ ( z) = ∑ n ≥ 0 ζ ′ ( − …
Polylogarithm function li
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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 … 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 …
WebCell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["PolyLog", "[", RowBox[List["n_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox ... WebThe functions Lin(z) are de ned on Cpnf1g. If Lis a nitely rami ed extension of Qpthen the limit limz!1 z2L Lin(z) exists for n 2, and is independent of L. Using this limit as the value for Lin at 1, Lin extends to a function on Cp, which is continuous on nitely rami ed extensions of Qp. If mand nare integers at least equal to 2, then on Cp
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 … WebFeb 3, 2024 · Integrals of inverse trigonometric and polylogarithmic functions. In this paper we study the representation of integrals whose integrand involves the product of a …
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 integrals. It …
WebThe 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. … ioss systemWebSep 18, 2024 · In this paper we study the representation of integrals whose integrand involves the product of a polylogarithm and an inverse or inverse hyperbolic trigonometric function. We further demonstrate many connections between these integrals and Euler sums. We develop recurrence relations and give some examples of these integrals in … onto complaintsWebJan 22, 2024 · Description. Compute the polylogarithm function Li_s (z) , initially defined as the power series, Li_ {s+1} (z) = Int [0..z] (Li_s (t) / t) dt. Currently, mainly the case of … ios ssh 免费WebIf Li s denotes the polylogarithm of order s, where s is a natural num- ... MSC: 11M35, 33E20, 40A25, 40B05. Keywords: Multiple harmonic series, Lerch function, Polylogarithm. Introduction Equalities and identities between multiple harmonic series and polyloga-rithms have been investigated by many authors; see for instance [1] and the ios star rating verticalWebThe 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 integrals. It also arises in the closed form of the integral of the Fermi-Dirac and the Bose-Einstein distributions. The special cases n=2 and n=3 are called the ... ios steam remote playWebPolylogarithm and Geometric Progression. Polylogarithm is connected to the infinite geometric progression sum \operatorname {Li}_0 (x)=\sum_ {n=1}^\infty x^n=\dfrac {x} {1 … onto cnnmoneyWebFeb 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) =: ∞ … on to crossword