Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalizing Ramanujan's J Functions   We generalize Ramanujan's expansions of the fractional-power Euler functions
(q^{1/5})_{\infty} = [ J_1 - q^{1/5} + q^{2/5} J_2 ](q^5)_{\infty} and
(q^{1/7})_{\infty} = [ J_1 + q^{1/7} J_2 - q^{2/7} + q^{5/7} J_3 ]
(q^7)_{\infty} to (q^{1/N})_{\infty}, where N is a prime number greater than 3.
We show that there are exactly (N+1)/2 non-zero J functions in the expansion of
(q^{1/N})_{\infty}, that one of these functions has the form +-q^{X_0}, that
all others have the form +-q^{X_k} times the ratio of two Ramanujan theta
functions, and that the product of all the non-zero J's is +-q^Z, where Z and
the X's denote non-negative integers.

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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: q-bio
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org