Summation algorithms for Stirling number identities. We consider a class of sequences defined by triangular recurrence equations. This class contains Stirling numbers and Eulerian numbers of both kinds, and hypergeometric multiples of those. We give a sufficient criterion for sums over such sequences to obey a recurrence equation, and present algorithms for computing such recurrence equations efficiently. Our algorithms can be used for verifying many known summation identities on Stirling numbers instantly, and also for discovering new identities.
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References in zbMATH (referenced in 9 articles , 1 standard article )
Showing results 1 to 9 of 9.
- Maltenfort, Michael: New definitions of the generalized Stirling numbers (2020)
- Jin, Hai-Tao: Formal residue and computer-assisted proofs of combinatorial identities (2018)
- Chen, Shaoshi; Kauers, Manuel: Some open problems related to creative telescoping (2017)
- Lee, Jen-Chi; Yan, Catherine H.; Yang, Yi: High-energy string scattering amplitudes and signless Stirling number identity (2012)
- Mu, Yan-Ping: Linear recurrence relations for sums of products of two terms (2011)
- Chen, William Y. C.; Sun, Lisa H.: Extended Zeilberger’s algorithm for identities on Bernoulli and Euler polynomials (2009)
- Chyzak, Frédéric; Kauers, Manuel; Salvy, Bruno: A non-holonomic systems approach to special function identities (2009)
- Kauers, Manuel; Schneider, Carsten: Automated proofs for some Stirling number identities (2008)
- Kauers, Manuel: Summation algorithms for Stirling number identities (2007)