Hyperlogarithm
In mathematics, the super-logarithm is one of the two inverse functions of tetration. Just as exponentiation has two inverse functions, roots and logarithms, tetration has two inverse functions, super-roots and super-logarithms. There are several ways of interpreting super-logarithms: As … Meer weergeven The super-logarithm, written $${\displaystyle \operatorname {slog} _{b}(z),}$$ is defined implicitly by $${\displaystyle \operatorname {slog} _{b}(b^{z})=\operatorname {slog} _{b}(z)+1}$$ Meer weergeven Usually, the special functions are defined not only for the real values of argument(s), but to complex plane, and differential and/or integral representation, as well as expansions in convergent and asymptotic series. Yet, no such representations are available for … Meer weergeven As tetration (or super-exponential) $${\displaystyle {\rm {sexp}}_{b}(z):={{^{z}}b}}$$ is suspected to be an … Meer weergeven The Abel function is any function that satisfies Abel's functional equation: $${\displaystyle A_{f}(f(x))=A_{f}(x)+1}$$ Given an Abel function $${\displaystyle A_{f}(x)}$$ another … Meer weergeven • Iterated logarithm • Tetration Meer weergeven • Rubstov and Romerio, Hyper-operations Thread 1 • Rubstov and Romerio, Hyper-operations Thread 2 Meer weergeven Web1 mrt. 2015 · Symbolic integration of such functions therefore serves a tool for the exact and direct evaluation of Feynman graphs. Solution method: Symbolic integration of rational …
Hyperlogarithm
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Web11 dec. 2016 · The hyperlogarithm \(L_w(z)\) is an iterated integral [12, 21] defined recursively in any simply connected open subset U of the punctured complex … Web6 dec. 2024 · Analogues of hyperlogarithm functions on affine complex curves. For a smooth affine complex curve, we show the existence and uniqueness of a minimal (for …
Web1 mrt. 2015 · In order to compute multi-dimensional integrals (1.4) by iterated integration using the algorithms of Section 2, we must require that for each k, the partial integral f k ∈ L (Σ k) (z k + 1) where Σ k ⊂ C (z k + 2, …, z n) is a hyperlogarithm in the next integration variable z k + 1. WebPlan of the talk Abstract Hyperlogarithms provide a tool to carry out numerous Feynman integrals. So far, this method has been applied successfully to finite single-scale process
WebWe provide algorithms for symbolic integration of hyperlogarithms multiplied by rational functions, which also include multiple polylogarithms when th… Webk is a hyperlogarithm in the next integra-tion variable z k+1. This criterion on f 0 is called linear reducibility in [11], where the symbolic integration algo-rithm of such functions is …
Web1 sep. 2016 · Given a formula for the Mahler measure of a rational function expressed in terms of polylogarithms, we describe a new method that allows us to construct a rational function with 2 more variables and whose Mahler measure is still expressed in terms of polylogarithms. We use this method to exhibit three new examples of Mahler measure …
Web6 dec. 2024 · Analogues of hyperlogarithm functions on affine complex curves 6 Dec 2024 · Benjamin Enriquez , Federico Zerbini · Edit social preview house chart ideasWebhyperlogarithm functions studied here. There is further motivation for studying hyperlogarithms with arbitrary singularities in quantum field theory, where … linn wealth managementWeb28 okt. 2024 · Multiple polylogarithm function and hyperlogarithm were introduced by Lappo- 15 Danilevski in 1927 [11], and subsequently rediscovered when evaluating … linn wiik facebookWebWe provide algorithms for symbolic integration of hyperlogarithms multiplied by rational functions, which also include multiple polylogarithms when their arguments are rational functions. These algorithms are implemented in Maple and we discuss various applications. In particular, many Feynman integrals can be computed by this method. house chart templateWeb3158 = ( (3 × 10 + 1) × 10 + 5) × 10 + 8. Although we don't normally think of it that way, the place-value notation avoids the unwieldy use of lots of symbols. When expressing larger numbers, like Avogadro's number and googol, one usually uses exponents and power towers, as discussed above: 6.02 × 10 23, 10 100 , 10 10100, 27 256312546656 ... linnwold.comWebAnalogues of hyperlogarithm functions on affine complex curves Joint with Benjamin Enriquez arXiv:2212.03119 [math.AG] Construction of Maurer-Cartan elements over configuration spaces of curves Joint with Benjamin Enriquez arXiv:2110.09341 [math.AG] Building blocks of closed and open string amplitudes Joint with Pierre Vanhove house chaser lubbockWebplural of hyperlogarithm 2016, Mikhail Kompaniets, Erik Panzer, “Renormalization group functions of ϕ 4 {\displaystyle \phi ^{4}} theory in the MS-scheme to six loops”, in arXiv[1]: … linnwinnpix.com