Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A generalized truncated logarithm   We introduce a generalization $G^{(\alpha)}(X)$ of the truncated logarithm
$\mathcal{L}_1(X) = \sum_{k=1}^{p-1}X^k/k$ in characteristic $p$, which depends
on a parameter $\alpha$. The main motivation of this study is $G^{(\alpha)}(X)$
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
$G^{(\alpha)}(X)$ motivated by known functional equations for
$\mathcal{L}_1(X)=-G^{(0)}(X)$.

21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: cmp-lg