We introduce a generalization G(α)(X) of the truncated logarithm £1(X)=∑k=1p-1Xk/k in prime characteristic p, which depends on a parameter α. The main motivation of this study is G(α)(X) being an inverse, in an appropriate sense, of a parametrized generalization of the truncated exponential given by certain Laguerre polynomials. Such Laguerre polynomials play a role in a grading switching technique for non-associative algebras, previously developed by the authors, because they satisfy a weak analogue of the functional equation exp (X) exp (Y) = exp (X+ Y) of the exponential series. We also investigate functional equations satisfied by G(α)(X) motivated by known functional equations for £ 1(X) = - G(0)(X).

Avitabile, M., Mattarei, S. (2019). A generalized truncated logarithm. AEQUATIONES MATHEMATICAE, 93(4), 711-734 [10.1007/s00010-018-0608-x].

A generalized truncated logarithm

Avitabile, M;Mattarei, S
2019

Abstract

We introduce a generalization G(α)(X) of the truncated logarithm £1(X)=∑k=1p-1Xk/k in prime characteristic p, which depends on a parameter α. The main motivation of this study is G(α)(X) being an inverse, in an appropriate sense, of a parametrized generalization of the truncated exponential given by certain Laguerre polynomials. Such Laguerre polynomials play a role in a grading switching technique for non-associative algebras, previously developed by the authors, because they satisfy a weak analogue of the functional equation exp (X) exp (Y) = exp (X+ Y) of the exponential series. We also investigate functional equations satisfied by G(α)(X) motivated by known functional equations for £ 1(X) = - G(0)(X).
Articolo in rivista - Articolo scientifico
Functional equation; Jacobi polynomial; Laguerre polynomial; Polylogarithm; Truncated logarithm;
Truncated logarithm Polylogarithm Laguerre polynomial Functional equation Jacobi polynomial
English
2019
93
4
711
734
reserved
Avitabile, M., Mattarei, S. (2019). A generalized truncated logarithm. AEQUATIONES MATHEMATICAE, 93(4), 711-734 [10.1007/s00010-018-0608-x].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/214513
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