WebJan 1, 1979 · Appendix A Spence functions The properties of Spence functions or dilogarithms are given in the literature [6], and we will present only a few equations. The defining equation is i SP (x) = - J dt In (lt xt) (A.1) 0 where the cut of the logarithm is along the negative real axis, implying for the Spence function a cut along the positive real ... WebMar 27, 2024 · special_spence () is used to compute element wise Spence’s integral of x. It is defined as the integral of log (t) / (1 – t) from 1 to x, with the domain of definition all …
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WebMar 7, 2024 · In mathematics, Spence's function, or dilogarithm, denoted as Li2(z), is a particular case of the polylogarithm. Two related special functions are referred to as Spence's function, the dilogarithm itself: Li 2 ( … In mathematics, Spence's function, or dilogarithm, denoted as Li2(z), is a particular case of the polylogarithm. Two related special functions are referred to as Spence's function, the dilogarithm itself: $${\displaystyle \operatorname {Li} _{2}(z)=-\int _{0}^{z}{\ln(1-u) \over u}\,du{\text{, }}z\in \mathbb {C} }$$and … See more Using the former definition above, the dilogarithm function is analytic everywhere on the complex plane except at $${\displaystyle z=1}$$, where it has a logarithmic branch point. The standard choice of branch cut … See more $${\displaystyle \operatorname {Li} _{2}(z)+\operatorname {Li} _{2}(-z)={\frac {1}{2}}\operatorname {Li} _{2}(z^{2}).}$$ See more Spence's Function is commonly encountered in particle physics while calculating radiative corrections. In this context, the function is often defined with an absolute value inside the logarithm: See more • NIST Digital Library of Mathematical Functions: Dilogarithm • Weisstein, Eric W. "Dilogarithm". MathWorld. See more $${\displaystyle \operatorname {Li} _{2}\left({\frac {1}{3}}\right)-{\frac {1}{6}}\operatorname {Li} _{2}\left({\frac {1}{9}}\right)={\frac {{\pi }^{2}}{18}}-{\frac {\ln ^{2}3}{6}}.}$$ See more • Bloch, Spencer J. (2000). Higher regulators, algebraic K-theory, and zeta functions of elliptic curves. CRM Monograph Series. Vol. 11. Providence, RI: American Mathematical Society See more butuff
Tail of Spence - Wikipedia
WebAbstract. An interesting connection exists between Spence's integral, used in Feynman diagrams in particle physics, and the variance of the reciprocal of a geometric random variable, used in probability theory. This linkage leads to approximate representations for Spence's integral over the unit interval which works well in practice. WebAug 26, 2016 · Spencer is a natural leader with a demonstrated ability of understanding the big picture and how he and his team contribute to an organizations growth as well as P&L. He has held increasingly progressive positions with prominent companies. His roles at each company were closely entrenched in the sales operations where he working day to day … WebNov 8, 2003 · Abstract. This paper summarizes the basic properties of the Euler dilogarithm function, often referred to as the Spence function. These include integral representations, … butuh in english