Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The iterated logarithmic algebra   We generalize the Umbral Calculus of G-C. Rota by studying not only sequences
of polynomials and inverse power series, or even the logarithms studied in, but
instead we study sequences of formal expressions involving the iterated
logarithms and x to an arbitrary real power.
  Using a theory of formal power series with real exponents, and a more general
definition of factorial, binomial coefficient, and Stirling numbers to all the
real numbers, we define the Iterated Logarithmic Algebra I. Its elements are
the formal representations of the asymptotic expansions of a large class of
real functions, and we define the harmonic logarithm basis of I which will be
interpreted as a generalization of the powers x^n since it behaves nicely with
respect to the derivative
  We classify all operators over I which commute with the derivative
(classically these are known as shift-invariant operators), and formulate
several equivalent definitions of a sequence of binomial type. We then derive
many formulas useful towards the calculation of these sequences including the
Recurrence Formula, the Transfer Formula, and the Lagrange Inversion Formula.
Finally, we study Sheffer sequences, and give many examples.

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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
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The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
26
The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th