A q-analogue of Graf's addition formula for the Hahn-Exton q-Bessel function

Mathematics – Classical Analysis and ODEs

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Scientific paper

An addition and product formula for the Hahn-Exton $q$-Bessel function,
previously obtained by use of a quantum group theoretic interpretation, are
proved analytically. A (formal) limit transition to the Graf addition formula
and corresponding product formula for the Bessel function is given.

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