Formal Proof of Transcendence of the Number e. Part II

[1] Alan Baker. Transcendental Number Theory. Cambridge University Press, 1990.Search in Google Scholar

[2] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.Open DOISearch in Google Scholar

[3] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.Open DOISearch in Google Scholar

[4] Sophie Bernard, Yves Bertot, Laurence Rideau, and Pierre-Yves Strub. Formal proofs of transcendence for e and π as an application of multivariate and symmetric polynomials. In Jeremy Avigad and Adam Chlipala, editors, Proceedings of the 5th ACM SIGPLAN Conference on Certified Programs and Proofs, pages 76–87. ACM, 2016. doi:10.1145/2854065.2854072.Open DOISearch in Google Scholar

[5] Jesse Bingham. Formalizing a proof that e is transcendental. Journal of Formalized Reasoning, 4:71–84, 2011.Search in Google Scholar

[6] Manuel Eberl. The transcendence of e. Archive of Formal Proofs, 2017. https://isa-afp.org/entries/E_Transcendental.html, Formal proof development.Search in Google Scholar

[7] Matsusaburo Fujiwara. Algebra vol 2, Japanese. Uchida Rokakuho Publishing Co., Ltd, 1st edition, 1929.Search in Google Scholar

[8] Adolf Hurwitz. Beweis der Transcendenz der Zahl e. Mathematische Annalen, 43:220–221, 1893.Search in Google Scholar

[9] Artur Korniłowicz. Elementary number theory problems. Part VIII. Formalized Mathematics, 31(1):87–100, 2023. doi:10.2478/forma-2023-0009.Open DOISearch in Google Scholar

[10] Artur Korniłowicz and Christoph Schwarzweller. The first isomorphism theorem and other properties of rings. Formalized Mathematics, 22(4):291–301, 2014. doi:10.2478/forma-2014-0029.Open DOISearch in Google Scholar

[11] Artur Korniłowicz, Adam Naumowicz, and Adam Grabowski. All Liouville numbers are transcendental. Formalized Mathematics, 25(1):49–54, 2017. doi:10.1515/forma-2017-0004.Open DOISearch in Google Scholar

[12] Serge Lang. Introduction to Transcendental Numbers. Addison-Wesley Pub. Co., 1966.Search in Google Scholar

[13] Norman D. Megill and David A. Wheeler. Metamath: A Computer Language for Mathematical Proofs. Lulu Press, Morrisville, North Carolina, 2019.Search in Google Scholar

[14] Robert Milewski. Fundamental theorem of algebra. Formalized Mathematics, 9(3):461–470, 2001.Search in Google Scholar

[15] Leonardo de Moura and Sebastian Ullrich. The Lean 4 theorem prover and programming language. In Automated Deduction – CADE 28: 28th International Conference on Automated Deduction, Virtual Event, July 12–15, 2021, Proceedings, pages 625–635, Berlin, Heidelberg, 2021. Springer-Verlag. doi:10.1007/978-3-030-79876-5 37.Open DOISearch in Google Scholar

[16] Karol P¡k. Eigenvalues of a linear transformation. Formalized Mathematics, 16(4):289–295, 2008. doi:10.2478/v10037-008-0035-x.Open DOISearch in Google Scholar

[17] Christoph Schwarzweller. On roots of polynomials over F [X]/[angbracketleft]p[angbracketright]. Formalized Mathematics, 27(2):93–100, 2019. doi:10.2478/forma-2019-0010.Open DOISearch in Google Scholar

[18] Christoph Schwarzweller. Normal extensions. Formalized Mathematics, 31(1):121–130, 2023. doi:10.2478/forma-2023-0011.Open DOISearch in Google Scholar

[19] Yasushige Watase. Formal proof of transcendence of the number e. Part I. Formalized Mathematics, 32(1):111–120, 2024. doi:10.2478/forma-2024-0008.Open DOISearch in Google Scholar

[20] Yasushige Watase. Derivation of commutative rings and the Leibniz formula for power of derivation. Formalized Mathematics, 29(1):1–8, 2021. doi:10.2478/forma-2021-0001.Open DOISearch in Google Scholar

[21] Freek Wiedijk. Formalizing 100 theorems. Available online at http://www.cs.ru.nl/~freek/100/.Search in Google Scholar