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MR2169800 (2009a:33029) 33F10 (65Q05) Mohammed, Mohamud; Zeilberger, Doron Sharp upper bounds for the orders of the recurrences output by the Zeilberger and $q$-Zeilberger algorithms. J. Symbolic Comput. 39 (2005), no. 2, 201--207.

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