Functional equations for higher logarithms
نویسندگان
چکیده
منابع مشابه
Functional Equations for Higher Logarithms
Following earlier work by Abel and others, Kummer gave functional equations for the polylogarithm function Lim(z) up to m = 5 in 1850, but no example for larger m was known until recently. We give the first genuine 2-variable functional equation for the 7–logarithm. We investigate and relate identities for the 3-logarithm given by Goncharov and Wojtkowiak and deduce a certain family of function...
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The (multivalued) higher logarithms are interpreted, by studying their monodromy, as giving well-defined maps from P¿ — (3 points} into certain complex nilmanifolds with C*-actions. The purpose of this note is to exhibit a family of unipotent representations of Z * Z arising naturally from the monodromy of the higher logarithms ln¿. (see [4]), and thereby interpret each ln¿. as yielding a well-...
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In this paper, using the recently introduced concept of periodic functions in quantum calculus, we study the existence of positive periodic solutions of a certain higher-order functional q-difference equation. Just as for the well-known continuous and discrete versions, we use a fixed point theorem in a cone in order to establish the existence of a positive periodic solution. This paper is dedi...
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In this paper, we apply a fixed point theorem to obtain sufficient conditions for the existence of positive periodic solutions for two classes of higher-order functional difference equations. AMS subject classification: 39A10.
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ژورنال
عنوان ژورنال: Selecta Mathematica
سال: 2003
ISSN: 1022-1824,1420-9020
DOI: 10.1007/s00029-003-0312-z