Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The fractional orthogonal derivative   This paper builds on the notion of the so-called orthogonal derivative, where
an n-th order derivative is approximated by an integral involving an orthogonal
polynomial of degree n. This notion was reviewed in great detail in a paper in
J. Approx. Theory (2012) by the author and Koornwinder. Here an approximation
of the Weyl or Riemann-Liouville fractional derivative is considered by
replacing the n-th derivative by its approximation in the formula for the
fractional derivative. In the case of, for instance, Jacobi polynomials an
explicit formula for the kernel of this approximate fractional derivative can
be given. Next we consider the fractional derivative as a filter and compute
the transfer function in the continuous case for the Jacobi polynomials and in
the discrete case for the Hahn polynomials. The transfer function in the Jacobi
case is a confluent hypergeometric function. A different approach is discussed
which starts with this explicit transfer function and then obtains the
approximate fractional derivative by taking the inverse Fourier transform. The
theory is finally illustrated with an application of a fractional
differentiating filter. In particular, graphs are presented of the absolute
value of the modulus of the transfer function. These make clear that for a good
insight in the behavior of a fractional differentiating filter one has to look
for the modulus of its transfer function in a log-log plot, rather than for
plots in the time domain.

27
The categories of this paper are: comp-gas
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
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The categories of this paper are: supr-con
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int