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).
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 From the seven unpublished manuscripts of H. W. Gould Edited and Compiled by Jocelyn Quaintance.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.