5. 参考文献#
5.1. 論文など#
論文
Ulrich Abel. New proofs of Melzak's identity. Aequationes mathematicae, 94(1):163–167, June 2019. URL: https://doi.org/10.1007/s00010-019-00659-4, doi:10.1007/s00010-019-00659-4.
Jordan Bell and Viktor Blåsjö. Pietro Mengoli's 1650 Proof that the Harmonic Series Diverges. Mathematics Magazine, 91(5):341–347, October 2018. URL: https://doi.org/10.1080/0025570x.2018.1506656, doi:10.1080/0025570x.2018.1506656.
Khristo N. Boyadzhiev. The formula of Melzak for arbitrary polynomials. 2017. arXiv:1701.01047.
Wenchang Chu. Harmonic number identities and Hermite–Padé approximations to the logarithm function. Journal of Approximation Theory, 137(1):42–56, November 2005. URL: https://doi.org/10.1016/j.jat.2005.07.008, doi:10.1016/j.jat.2005.07.008.
Antonio J. Duran, R. J. Chapman, and R. W. K. Odoni. E3339. The American Mathematical Monthly, 98(3):269, March 1991. URL: https://doi.org/10.2307/2325039, doi:10.2307/2325039.
Ira Gessel. Generating Functions and Generalized Dedekind Sums. The Electronic Journal of Combinatorics, October 1996. URL: https://doi.org/10.37236/1326, doi:10.37236/1326.
Z. A. Melzak, V. D. Gokhale, and W. V. Parker. 4458. The American Mathematical Monthly, 60(1):53–54, January 1953. URL: https://doi.org/10.2307/2306491, doi:10.2307/2306491.
Jun-Ming Zhu and Qiu-Ming Luo. A novel proof of two partial fraction decompositions. Advances in Difference Equations, June 2021. URL: https://doi.org/10.1186/s13662-021-03433-6, doi:10.1186/s13662-021-03433-6.
書籍
Ernst Hairer and Gerhard Wanner. 解析教程 上 新装版, pages 141–146. シュプリンガー・ジャパン, October 2006, 蟹江 幸博 (訳).
堀口 剛, 海老澤 丕道, and 福井 芳彦. 応用数学講義, pages 292–294. 培風館, March 2000.
神保 道夫. 複素関数入門, pages 97–99. 現代数学への入門 新装版. 岩波書店, October 2024.
ウェブページ
Analysis Fact (@AnalysisFact). Apr 2023. URL: https://twitter.com/AnalysisFact/status/1642135084839976961.
Henry W. Gould and Jocelyn Quaintance. Combinatorial Identities: Table II: Advanced Techniques for Summing Finite Series. From the seven unpublished manuscripts of H. W. Gould Edited and Compiled by Jocelyn Quaintance. May 2010. URL: https://math.wvu.edu/~hgould/Vol.5.PDF.
mathcam. Product rule. Mar 2013. URL: https://planetmath.org/productrule.
stevecheng. Partial fractions for polynomials. Mar 2013. URL: https://planetmath.org/partialfractionsforpolynomials.
Eric W. Weisstein. Faà di Bruno's Formula. From MathWorld—A Wolfram Web Resource. URL: https://mathworld.wolfram.com/FaadiBrunosFormula.html.
Eric W. Weisstein. Leibniz Identity. From MathWorld—A Wolfram Web Resource. URL: https://mathworld.wolfram.com/LeibnizIdentity.html.
Eric W. Weisstein. Product Rule. From MathWorld—A Wolfram Web Resource. URL: https://mathworld.wolfram.com/ProductRule.html.