Formal residue and computer-assisted proofs of combinatorial identities

DOI10.3906/mat-1804-42zbMath1424.33040OpenAlexW2893772705WikidataQ113692764 ScholiaQ113692764MaRDI QIDQ5742818

Hai-Tao Jin

Publication date: 8 May 2019

Published in: TURKISH JOURNAL OF MATHEMATICS (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3906/mat-1804-42

zbMATH Keywords

Stirling numberformal residueextended Zeilberger algorithm

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Bell and Stirling numbers (11B73) Combinatorial identities, bijective combinatorics (05A19) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

Uses Software

• Stirling

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The extended Zeilberger algorithm with parameters
• Linear recurrence relations for sums of products of two terms
• An algorithmic proof theory for hypergeometric (ordinary and ``\(q\)) multisum/integral identities
• Automated proofs for some Stirling number identities
• Extended Zeilberger's algorithm for identities on Bernoulli and Euler polynomials
• Operatormethoden für q-identitäten
• The method of creative telescoping
• Non-commutative elimination in Ore algebras proves multivariate identities
• Computer proofs of a new family of harmonic number identities.
• Some applications of the \(q\)-exponential formula
• An extension of Zeilberger's fast algorithm to general holonomic functions
• Summation algorithms for Stirling number identities
• A non-holonomic systems approach to special function identities
• Advanced applications of the holonomic systems approach