q-Abel-Zeilberger算法与q-超调和数恒等式
q-Abel-Zeilberger Algorithm and q-Hyperharmonic Numbers Identities
摘要: 本文将Abel引理与q-Zeilberger算法相结合来研究q-非超几何和式。对一类含有q-超调和数的相关和式,得到了一些新的q-模拟恒等式。
Abstract: This article combines Abel’s lemma with q-Zeilberger algorithm to study q-non-hypergeometric sums. For a class of related sum of q-hyperharmonic numbers, some new q-analogous identities are obtained.
文章引用:周梦肖. q-Abel-Zeilberger算法与q-超调和数恒等式[J]. 理论数学, 2024, 14(10): 101-107. https://doi.org/10.12677/pm.2024.1410349

参考文献

[1] Boyadzhiev, K.N. (2014) Binomial Transform and the Backward Difference. Mathematics, 13, 43-63.
[2] Chen, K. and Chen, Y. (2020) Infinite Series Containing Generalized Harmonic Functions. Notes on Number Theory and Discrete Mathematics, 26, 85-104. [Google Scholar] [CrossRef
[3] Chu, W. and De Donno, L. (2005) Hypergeometric Series and Harmonic Number Identities. Advances in Applied Mathematics, 34, 123-137. [Google Scholar] [CrossRef
[4] Frontczak, R. (2021) Binomial Sums with Skew-Harmonic Numbers. Palestine Journal of Mathematics, 10, 756-763.
[5] Guo, D.W. (2022) Some Combinatorial Identities Concerning Harmonic Numbers and Binomial Coefficients. Discrete Mathematics Letters, 8, 41-48.
[6] Conway, J.H. and Guy, R.K. (1996) The Book of Numbers. Copernicus.
[7] Mansour, T., Mansour, M. and Song, C.W. (2012) q-Analogs of Identities Involving Harmonic Numbers and Binomial Coefficients. Applications and Applied Mathematics, 7, 22-36.
[8] Mansour, T. and Shattuck, M. (2012) A q-Analog of the Hyperharmonic Numbers. Afrika Matematika, 25, 147-160. [Google Scholar] [CrossRef
[9] Kızılates, C. and Tuğlu, N. (2015) Some Combinatorial Identities of q-Harmonic and q-Hyperharmonic Numbers. Communications in Mathematics and Applications, 6, 33-40.
[10] Chen, W.Y.C., Hou, Q. and Jin, H. (2011) The Abel-Zeilberger Algorithm. The Electronic Journal of Combinatorics, 18, Article No. 17. [Google Scholar] [CrossRef
[11] Xu, J. and Ma, X. (2024) General q-Series Transformations Based on Abel’s Lemma on Summation by Parts and Their Applications. Journal of Difference Equations and Applications, 30, 553-576. [Google Scholar] [CrossRef
[12] Chu, W. and Wang, C. (2009) Abel’s Lemma on Summation by Parts and Partial Q-Series Transformations. Science in China Series A: Mathematics, 52, 720-748. [Google Scholar] [CrossRef
[13] Petkovsěk, M., Wilf, H.S. and Zeilberger, D. (1996) A = B. A.K. Peters Ltd.