For three families of nonlinear recurrences, the paper gives asymptotic expansions and high-precision numerical constants, including a new reciprocity relation for the q=3/2 case.
Popa's "Recurrent Sequences" and Reciprocity
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abstract
Dumitru Popa found asymptotic expansions for certain nonlinear recurrences, but left open the numerical evaluation of associated constants. We address this issue. A change of variables involving reciprocals and the algorithm of Mavecha & Laohakosol play a key role in our computations.
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Exercises in Iterational Asymptotics
For three families of nonlinear recurrences, the paper gives asymptotic expansions and high-precision numerical constants, including a new reciprocity relation for the q=3/2 case.