In mathematics, the dilogarithm (or Spence's function), denoted as Li2(z), is a particular case of the polylogarithm. Two related special functions are...

Li1(z) = −ln(1−z), while the special cases s = 2 and s = 3 are called the dilogarithm (also referred to as Spence's function) and trilogarithm respectively...

In mathematics, the quantum dilogarithm is a special function defined by the formula ϕ ( x ) ≡ ( x ; q ) ∞ = ∏ n = 0 ∞ ( 1 − x q n ) , | q | < 1 {\displaystyle...

_{2}(y^{2}){\biggr ]}_{y=0}^{y=1}={\frac {3}{2}}\,\mathrm {Li} _{2}(1)} For the Dilogarithm of one this value appears: L i 2 ( 1 ) = π 2 6 {\displaystyle \mathrm...

Askey–Wilson operators. The q-exponential is also known as the quantum dilogarithm. The q-exponential e q ( z ) {\displaystyle e_{q}(z)} is defined as e...

\xi (z)=\xi (1-z).} Weisstein, Eric W. "Dilogarithm". mathworld.wolfram.com. Retrieved 2024-08-01. "Dilogarithm Reflection Formula - ProofWiki". proofwiki...

Equivalently, it can be defined by a power series, or in terms of the dilogarithm, a closely related special function. The inverse tangent integral is...

Faddeev–Senjanovic quantization Faddeev–Jackiw quantization Quantum dilogarithm Quantum inverse scattering method Yangian Awards Dannie Heineman Prize...

Complete Fermi–Dirac integral, an alternate form of the polylogarithm. Dilogarithm Incomplete Fermi–Dirac integral Kummer's function Riesz function Hypergeometric...

1995 for hyperbolic links as a state sum using the theory of quantum dilogarithms. Kashaev stated the formula of the volume conjecture in the case of hyperbolic...

L_{2}(x)=-\int _{0}^{x}{\frac {\ln(1-t)}{t}}\operatorname {d} \!t} (the dilogarithm) to nine decimal places, in a table, for all integer values of 1 + x...

calculus Time scale calculus q-analog Basic hypergeometric series Quantum dilogarithm Abreu, Luis Daniel (2006). "Functions q-Orthogonal with Respect to Their...

zeta function of an arbitrary number field at s = 2 in terms of the dilogarithm function, by studying arithmetic hyperbolic 3-manifolds. He later formulated...

(with V. V. Fock) Fock, V.V.; Goncharov, A.B. (2009). "The quantum dilogarithm and representations of quantum cluster varieties". Inventiones Mathematicae...

is equal to g(z)/z with g of Example 2. It turns out that h(z) is the dilogarithm function. Example 4: The power series ∑ i = 1 ∞ a i z i  where  a i =...

ez, log z, cos z, arcsin z, 1 + z {\displaystyle {\sqrt {1+z}}} , the dilogarithm function Li2(z), the generalized hypergeometric functions pFq(...; ....

_{2}(x)=\sum _{n>0}\,{x^{n}}{n^{-2}}=x\;{}_{3}F_{2}(1,1,1;2,2;x)} is the dilogarithm The function Q n ( x ; a , b , N ) = 3 F 2 ( − n , − x , n + a + b +...

quickly for large n. An expansion may also be given in terms of the dilogarithm: ln ⁡ K 0 2 = 1 ln ⁡ 2 [ Li 2 ( − 1 2 ) + 1 2 ∑ k = 2 ∞ ( − 1 ) k Li...

can be expressed in terms of the Lobachevsky function, or in terms of dilogarithms. Hugo Hadwiger conjectured in 1956 that every simplex can be dissected...

}{2}}\right)\right]} , where Li 2 {\displaystyle \operatorname {Li} _{2}} is the dilogarithm and i = − 1 {\displaystyle i={\sqrt {-1}}} is the imaginary unit. If...

Goncharov, A. B.; Schechtman, V. V.; Varchenko, A. N. (1990). "Aomoto dilogarithms, mixed Hodge structures and motivic cohomology of pairs of triangles...

Boyd, David (2002b). "Mahler's measure, hyperbolic manifolds and the dilogarithm". Canadian Mathematical Society Notes. 34 (2): 3–4, 26–28. Boyd, David;...

on Reactive Elements for Broad-Band Impedance Matching (1952, author) Dilogarithms and Associated Functions (1958, author) Explanatory notes on the use...

simple terms, which can be integrated analytically through use of the dilogarithm function. Mathematics portal Integration by substitution Trigonometric...

Fortran 77 code Fortran 90 version Maximon, Leonard C. (2003). "The dilogarithm function for complex argument". Proc. R. Soc. A. 459 (2039): 2807–2819...

{Li_{2}} [-(r-1)]} where L i 2 {\displaystyle \mathrm {Li_{2}} } is the dilogarithm function. G equation Matalon–Matkowsky–Clavin–Joulin theory Clavin–Garcia...

Bernoulli number, L i 2 ( z ) {\displaystyle \mathrm {Li} _{2}(z)} is the dilogarithm, and p k {\displaystyle p_{k}} is a polynomial of degree k {\displaystyle...

Chicago. Accessed January 12, 2010 Bloch, S. (1978). "Applications of the dilogarithm function in algebraic K-theory and algebraic geometry". In Nagata, M...

related to polylogarithm, hyperbolic geometry and algebraic K-theory. The dilogarithm function is the function defined by the power series Li 2 ⁡ ( z ) = ∑...

x_{0}})}}} where Li 2 {\displaystyle \operatorname {Li} _{2}} is the dilogarithm function Let U be a random variate from the standard uniform distribution...