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...

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...

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...

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

_{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...

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...

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

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...

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 =...

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

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

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

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

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...

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

}{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...

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

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

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...

_{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 +...

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...

{Li} _{2}(1-u)+{\frac {\pi ^{2}}{12}}.} with Li2 the dilogarithm. Other ρ n {\displaystyle \rho _{n}} can be calculated using infinite...

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

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

Peters 2000, pp. 127–143 Mahler's measure, hyperbolic manifolds and the dilogarithm, Canadian Mathematical Society Notes, vol. 34, no. 2, 2002, 3–4, 26–28...

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...