Proof of unsolvability of $q$-Bessel equation using valuations

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JMS
Vol. 23 (2016), No. 4, Page 763–789.

Nishioka, Seiji
Proof of unsolvability of $q$-Bessel equation using valuations
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Abstract:
In this paper, we prove unsolvability of the $q$-Bessel equation associated with one of the $q$-Bessel functions, $J_\nu^{(3)}$, using the notion of the difference field extension of valuation ring type.

Keywords: solvability, algebraic independence.

Mathematics Subject Classification (2010): 12H10, 39A13

Mathematical Reviews Number: MR3588262

Received: 2015-09-08

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