Complete reductions can be built recursively in towers of Sigma*-extensions, yielding faster refined and parameterized telescoping algorithms for nested harmonic sums.
The Absent-Minded Passengers Problem: A Motivating Challenge Solved by Computer Algebra
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In (S.B. Ekhad and D. Zeilberger, 2020) an exciting case study has been initiated in which experimental mathematics and symbolic computation are utilized to discover new properties concerning the so-called Absent-Minded Passengers Problem. Based on these results, Doron Zeilberger raised some challenging tasks to gain further probabilistic insight. In this note we report on this enterprise. In particular, we demonstrate how the computer algebra packages of RISC can be used to carry out the underlying heavy calculations.
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Telescoping Algorithms for $\Sigma^*$-Extensions via Complete Reductions
Complete reductions can be built recursively in towers of Sigma*-extensions, yielding faster refined and parameterized telescoping algorithms for nested harmonic sums.