Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Central differences, Euler numbers and symbolic methods   I relate some coefficients encountered when computing the functional
determinants on spheres to the central differentials of nothing. In doing this
I use some historic works, in particular transcribing the elegant symbolic
formalism of Jeffery (1861) into central difference form which has
computational advantages for Euler numbers, as discovered by Shovelton (1915).
I derive sum rules for these, and for the central differentials, the proof of
which involves an interesting expression for powers of sech x as multiple
derivatives. I present a more general, symbolic treatment of central difference
calculus which allows known, and unknown, things to be obtained in an elegant
and compact fashion gaining, at no cost, the expansion of the powers of the
inverse sinh, a basic central function. Systematic use is made of the operator
2 asinh(D/2). Umbral calculus is employed to compress the operator formalism.
For example the orthogonality/completeness of the factorial numbers, of the
first and second kinds, translates, umbrally, to T(t(x))=x. The classic
expansions of multiple angle cosh and sinh in terms of powers of sinh are
thence obtained with minimal effort.

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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph