Transcendental number (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Transcendental number" in English language version.

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Allouche, Jean-Paul; Cosnard, Michel (2000), "The Komornik–Loreti constant is transcendental", American Mathematical Monthly, 107 (5): 448–449, doi:10.2307/2695302, JSTOR 2695302, MR 1763399
Blanchard & Mendès France 1982 Blanchard, André; Mendès France, Michel (1982). "Symétrie et transcendance". Bulletin des Sciences Mathématiques. 106 (3): 325–335. MR 0680277.

archive.org

Leibniz, Gerhardt & Pertz 1858, pp. 97–98; Bourbaki 1994, p. 74 Leibniz, G.W.; Gerhardt, Karl Immanuel; Pertz, Georg Heinrich (1858). Leibnizens mathematische Schriften. Vol. 5. A. Asher & Co. pp. 97–98 – via Internet Archive. Bourbaki, N. (1994). Elements of the History of Mathematics. Springer. ISBN 9783540647676 – via Internet Archive.

arxiv.org

Heuer, Nicolaus; Loeh, Clara (1 November 2019). "Transcendental simplicial volumes". arXiv:1911.06386 [math.GT].
Adamczewski & Bugeaud 2005 Adamczewski, Boris; Bugeaud, Yann (2005). "On the complexity of algebraic numbers, II. Continued fractions". Acta Mathematica. 195 (1): 1–20. arXiv:math/0511677. Bibcode:2005math.....11677A. doi:10.1007/BF02588048. S2CID 15521751.
Mező, István; Baricz, Árpád (June 22, 2015). "On the generalization of the Lambert W function". arXiv:1408.3999 [math.CA].
Lagarias, Jeffrey C. (2013-07-19). "Euler's constant: Euler's work and modern developments". Bulletin of the American Mathematical Society. 50 (4): 527–628. arXiv:1303.1856. doi:10.1090/S0273-0979-2013-01423-X. ISSN 0273-0979.
Yoshinaga, Masahiko (2008-05-03). "Periods and elementary real numbers". arXiv:0805.0349 [math.AG].
Adamczewski, Boris (March 2013). "The Many Faces of the Kempner Number". arXiv:1303.1685 [math.NT].
van de Pol, Levi (2022). "The first occurrence of a number in Gijswijt's sequence". arXiv:2209.04657 [math.CO].

books.google.com

Bunday, B. D.; Mulholland, H. (20 May 2014). Pure Mathematics for Advanced Level. Butterworth-Heinemann. ISBN 978-1-4831-0613-7. Retrieved 21 March 2021.

britannica.com

"Real number". Encyclopædia Britannica. mathematics. Retrieved 2020-08-11.

cambridge.org

Adamczewski, Boris; Rivoal, Tanguy (2009). "Irrationality measures for some automatic real numbers". Mathematical Proceedings of the Cambridge Philosophical Society. 147 (3): 659–678. Bibcode:2009MPCPS.147..659A. doi:10.1017/S0305004109002643. ISSN 1469-8064.
"Mathematical constants". Mathematics (general). Cambridge University Press. Retrieved 2022-09-22.

digizeitschriften.de

Cantor 1874; Gray 1994 Cantor, G. (1874). "Über eine Eigenschaft des Inbegriffes aller reelen algebraischen Zahlen". J. Reine Angew. Math. 77: 258–262. Gray, Robert (1994). "Georg Cantor and transcendental numbers". Amer. Math. Monthly. 101 (9): 819–832. doi:10.2307/2975129. JSTOR 2975129. Zbl 0827.01004 – via maa.org.
Cantor 1878, p. 254 Cantor, G. (1878). "Ein Beitrag zur Mannigfaltigkeitslehre". J. Reine Angew. Math. 84: 242–258.

doi.org

Baker, A. (1964). "On Mahler's classification of transcendental numbers". Acta Mathematica. 111: 97–120. doi:10.1007/bf02391010. S2CID 122023355.
Erdős & Dudley 1983 Erdős, P.; Dudley, U. (1983). "Some Remarks and Problems in Number Theory Related to the Work of Euler" (PDF). Mathematics Magazine. 56 (5): 292–298. CiteSeerX 10.1.1.210.6272. doi:10.2307/2690369. JSTOR 2690369.
Kempner 1916 Kempner, Aubrey J. (1916). "On Transcendental Numbers". Transactions of the American Mathematical Society. 17 (4): 476–482. doi:10.2307/1988833. JSTOR 1988833.
Cantor 1874; Gray 1994 Cantor, G. (1874). "Über eine Eigenschaft des Inbegriffes aller reelen algebraischen Zahlen". J. Reine Angew. Math. 77: 258–262. Gray, Robert (1994). "Georg Cantor and transcendental numbers". Amer. Math. Monthly. 101 (9): 819–832. doi:10.2307/2975129. JSTOR 2975129. Zbl 0827.01004 – via maa.org.
Adamczewski & Bugeaud 2005 Adamczewski, Boris; Bugeaud, Yann (2005). "On the complexity of algebraic numbers, II. Continued fractions". Acta Mathematica. 195 (1): 1–20. arXiv:math/0511677. Bibcode:2005math.....11677A. doi:10.1007/BF02588048. S2CID 15521751.
Nesterenko, Yu V (1996-10-31). "Modular functions and transcendence questions". Sbornik: Mathematics. 187 (9): 1319–1348. Bibcode:1996SbMat.187.1319N. doi:10.1070/SM1996v187n09ABEH000158. ISSN 1064-5616.
Siegel, Carl L. (2014). "Über einige Anwendungen diophantischer Approximationen: Abhandlungen der Preußischen Akademie der Wissenschaften. Physikalisch-mathematische Klasse 1929, Nr. 1". On Some Applications of Diophantine Approximations (in German). Scuola Normale Superiore. pp. 81–138. doi:10.1007/978-88-7642-520-2_2. ISBN 978-88-7642-520-2.
Lorch, Lee; Muldoon, Martin E. (1995). "Transcendentality of zeros of higher dereivatives of functions involving Bessel functions". International Journal of Mathematics and Mathematical Sciences. 18 (3): 551–560. doi:10.1155/S0161171295000706.
Mahler, Kurt; Mordell, Louis Joel (1968-06-04). "Applications of a theorem by A. B. Shidlovski". Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 305 (1481): 149–173. Bibcode:1968RSPSA.305..149M. doi:10.1098/rspa.1968.0111. S2CID 123486171.
Lagarias, Jeffrey C. (2013-07-19). "Euler's constant: Euler's work and modern developments". Bulletin of the American Mathematical Society. 50 (4): 527–628. arXiv:1303.1856. doi:10.1090/S0273-0979-2013-01423-X. ISSN 0273-0979.
Mahler 1929; Allouche & Shallit 2003, p. 387 Mahler, K. (1929). "Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen". Math. Annalen. 101: 342–366. doi:10.1007/bf01454845. JFM 55.0115.01. S2CID 120549929. Allouche, J.-P. [in French]; Shallit, J. (2003). Automatic Sequences: Theory, applications, generalizations. Cambridge University Press. ISBN 978-0-521-82332-6. Zbl 1086.11015.
Allouche, Jean-Paul; Cosnard, Michel (2000), "The Komornik–Loreti constant is transcendental", American Mathematical Monthly, 107 (5): 448–449, doi:10.2307/2695302, JSTOR 2695302, MR 1763399
Adamczewski, Boris; Rivoal, Tanguy (2009). "Irrationality measures for some automatic real numbers". Mathematical Proceedings of the Cambridge Philosophical Society. 147 (3): 659–678. Bibcode:2009MPCPS.147..659A. doi:10.1017/S0305004109002643. ISSN 1469-8064.
Kurosawa, Takeshi (2007-03-01). "Transcendence of certain series involving binary linear recurrences". Journal of Number Theory. 123 (1): 35–58. doi:10.1016/j.jnt.2006.05.019. ISSN 0022-314X.
Duverney, Daniel; Nishioka, Keiji; Nishioka, Kumiko; Shiokawa, Iekata (1997). "Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers". Proceedings of the Japan Academy, Series A, Mathematical Sciences. 73 (7): 140–142. doi:10.3792/pjaa.73.140. ISSN 0386-2194.
Bertrand, Daniel (1997). "Theta functions and transcendence". The Ramanujan Journal. 1 (4): 339–350. doi:10.1023/A:1009749608672. S2CID 118628723.
Bailey, David H. (1988). "Numerical Results on the Transcendence of Constants Involving $\pi, e$, and Euler's Constant". Mathematics of Computation. 50 (181): 275–281. doi:10.2307/2007931. ISSN 0025-5718. JSTOR 2007931.
Brownawell, W. Dale (1974-02-01). "The algebraic independence of certain numbers related by the exponential function". Journal of Number Theory. 6 (1): 22–31. Bibcode:1974JNT.....6...22B. doi:10.1016/0022-314X(74)90005-5. ISSN 0022-314X.
Murty, M. Ram; Saradha, N. (2010-12-01). "Euler–Lehmer constants and a conjecture of Erdös". Journal of Number Theory. 130 (12): 2671–2682. doi:10.1016/j.jnt.2010.07.004. ISSN 0022-314X.
Murty, M. Ram; Zaytseva, Anastasia (2013-01-01). "Transcendence of generalized Euler constants". The American Mathematical Monthly. 120 (1): 48–54. doi:10.4169/amer.math.monthly.120.01.048. ISSN 0002-9890. S2CID 20495981.
Rivoal, Tanguy (2012). "On the arithmetic nature of the values of the gamma function, Euler's constant, and Gompertz's constant". Michigan Mathematical Journal. 61 (2): 239–254. doi:10.1307/mmj/1339011525. ISSN 0026-2285.
Rivoal, T.; Zudilin, W. (2003-08-01). "Diophantine properties of numbers related to Catalan's constant". Mathematische Annalen. 326 (4): 705–721. doi:10.1007/s00208-003-0420-2. hdl:1959.13/803688. ISSN 1432-1807. S2CID 59328860.

handle.net

hdl.handle.net

Rivoal, T.; Zudilin, W. (2003-08-01). "Diophantine properties of numbers related to Catalan's constant". Mathematische Annalen. 326 (4): 705–721. doi:10.1007/s00208-003-0420-2. hdl:1959.13/803688. ISSN 1432-1807. S2CID 59328860.

harvard.edu

ui.adsabs.harvard.edu

Adamczewski & Bugeaud 2005 Adamczewski, Boris; Bugeaud, Yann (2005). "On the complexity of algebraic numbers, II. Continued fractions". Acta Mathematica. 195 (1): 1–20. arXiv:math/0511677. Bibcode:2005math.....11677A. doi:10.1007/BF02588048. S2CID 15521751.
Nesterenko, Yu V (1996-10-31). "Modular functions and transcendence questions". Sbornik: Mathematics. 187 (9): 1319–1348. Bibcode:1996SbMat.187.1319N. doi:10.1070/SM1996v187n09ABEH000158. ISSN 1064-5616.
Mahler, Kurt; Mordell, Louis Joel (1968-06-04). "Applications of a theorem by A. B. Shidlovski". Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 305 (1481): 149–173. Bibcode:1968RSPSA.305..149M. doi:10.1098/rspa.1968.0111. S2CID 123486171.
Adamczewski, Boris; Rivoal, Tanguy (2009). "Irrationality measures for some automatic real numbers". Mathematical Proceedings of the Cambridge Philosophical Society. 147 (3): 659–678. Bibcode:2009MPCPS.147..659A. doi:10.1017/S0305004109002643. ISSN 1469-8064.
Brownawell, W. Dale (1974-02-01). "The algebraic independence of certain numbers related by the exponential function". Journal of Number Theory. 6 (1): 22–31. Bibcode:1974JNT.....6...22B. doi:10.1016/0022-314X(74)90005-5. ISSN 0022-314X.

imj-prg.fr

webusers.imj-prg.fr

Waldschmidt, Michel (September 7, 2005). "Transcendence of Periods: The State of the Art" (PDF). webusers.imj-prg.fr.
Waldschmidt, Michel (2021). "Schanuel's Conjecture: algebraic independence of transcendental numbers" (PDF).
Waldschmidt, Michel (2022). "Transcendental Number Theory: recent results and open problems". Michel Waldschmidt.

iop.org

iopscience.iop.org

Nesterenko, Yu V (1996-10-31). "Modular functions and transcendence questions". Sbornik: Mathematics. 187 (9): 1319–1348. Bibcode:1996SbMat.187.1319N. doi:10.1070/SM1996v187n09ABEH000158. ISSN 1064-5616.

jstor.org

Erdős & Dudley 1983 Erdős, P.; Dudley, U. (1983). "Some Remarks and Problems in Number Theory Related to the Work of Euler" (PDF). Mathematics Magazine. 56 (5): 292–298. CiteSeerX 10.1.1.210.6272. doi:10.2307/2690369. JSTOR 2690369.
Kempner 1916 Kempner, Aubrey J. (1916). "On Transcendental Numbers". Transactions of the American Mathematical Society. 17 (4): 476–482. doi:10.2307/1988833. JSTOR 1988833.
Cantor 1874; Gray 1994 Cantor, G. (1874). "Über eine Eigenschaft des Inbegriffes aller reelen algebraischen Zahlen". J. Reine Angew. Math. 77: 258–262. Gray, Robert (1994). "Georg Cantor and transcendental numbers". Amer. Math. Monthly. 101 (9): 819–832. doi:10.2307/2975129. JSTOR 2975129. Zbl 0827.01004 – via maa.org.
Allouche, Jean-Paul; Cosnard, Michel (2000), "The Komornik–Loreti constant is transcendental", American Mathematical Monthly, 107 (5): 448–449, doi:10.2307/2695302, JSTOR 2695302, MR 1763399
Bailey, David H. (1988). "Numerical Results on the Transcendence of Constants Involving $\pi, e$, and Euler's Constant". Mathematics of Computation. 50 (181): 275–281. doi:10.2307/2007931. ISSN 0025-5718. JSTOR 2007931.

maa.org

Cantor 1874; Gray 1994 Cantor, G. (1874). "Über eine Eigenschaft des Inbegriffes aller reelen algebraischen Zahlen". J. Reine Angew. Math. 77: 258–262. Gray, Robert (1994). "Georg Cantor and transcendental numbers". Amer. Math. Monthly. 101 (9): 819–832. doi:10.2307/2975129. JSTOR 2975129. Zbl 0827.01004 – via maa.org.

mathdoc.fr

sites.mathdoc.fr

Liouville 1851 Liouville, J. (1851). "Sur des classes très étendues de quantités dont la valeur n'est ni algébrique, ni même réductible à des irrationnelles algébriques" (PDF). J. Math. Pures Appl. 16: 133–142.

oed.com

"transcendental". Oxford English Dictionary. s.v.

oeis.org

"A143347 - OEIS". oeis.org. Retrieved 2023-08-09.
"A140654 - OEIS". oeis.org. Retrieved 2023-08-12.

projecteuclid.org

Rivoal, Tanguy (2012). "On the arithmetic nature of the values of the gamma function, Euler's constant, and Gompertz's constant". Michigan Mathematical Journal. 61 (2): 239–254. doi:10.1307/mmj/1339011525. ISSN 0026-2285.

psu.edu

citeseerx.ist.psu.edu

Erdős & Dudley 1983 Erdős, P.; Dudley, U. (1983). "Some Remarks and Problems in Number Theory Related to the Work of Euler" (PDF). Mathematics Magazine. 56 (5): 292–298. CiteSeerX 10.1.1.210.6272. doi:10.2307/2690369. JSTOR 2690369.

renyi.hu

users.renyi.hu

Erdős & Dudley 1983 Erdős, P.; Dudley, U. (1983). "Some Remarks and Problems in Number Theory Related to the Work of Euler" (PDF). Mathematics Magazine. 56 (5): 292–298. CiteSeerX 10.1.1.210.6272. doi:10.2307/2690369. JSTOR 2690369.

royalsocietypublishing.org

Mahler, Kurt; Mordell, Louis Joel (1968-06-04). "Applications of a theorem by A. B. Shidlovski". Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 305 (1481): 149–173. Bibcode:1968RSPSA.305..149M. doi:10.1098/rspa.1968.0111. S2CID 123486171.

semanticscholar.org

api.semanticscholar.org

Baker, A. (1964). "On Mahler's classification of transcendental numbers". Acta Mathematica. 111: 97–120. doi:10.1007/bf02391010. S2CID 122023355.
Adamczewski & Bugeaud 2005 Adamczewski, Boris; Bugeaud, Yann (2005). "On the complexity of algebraic numbers, II. Continued fractions". Acta Mathematica. 195 (1): 1–20. arXiv:math/0511677. Bibcode:2005math.....11677A. doi:10.1007/BF02588048. S2CID 15521751.
Mahler, Kurt; Mordell, Louis Joel (1968-06-04). "Applications of a theorem by A. B. Shidlovski". Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences. 305 (1481): 149–173. Bibcode:1968RSPSA.305..149M. doi:10.1098/rspa.1968.0111. S2CID 123486171.
Mahler 1929; Allouche & Shallit 2003, p. 387 Mahler, K. (1929). "Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen". Math. Annalen. 101: 342–366. doi:10.1007/bf01454845. JFM 55.0115.01. S2CID 120549929. Allouche, J.-P. [in French]; Shallit, J. (2003). Automatic Sequences: Theory, applications, generalizations. Cambridge University Press. ISBN 978-0-521-82332-6. Zbl 1086.11015.
Bertrand, Daniel (1997). "Theta functions and transcendence". The Ramanujan Journal. 1 (4): 339–350. doi:10.1023/A:1009749608672. S2CID 118628723.
Murty, M. Ram; Zaytseva, Anastasia (2013-01-01). "Transcendence of generalized Euler constants". The American Mathematical Monthly. 120 (1): 48–54. doi:10.4169/amer.math.monthly.120.01.048. ISSN 0002-9890. S2CID 20495981.
Rivoal, T.; Zudilin, W. (2003-08-01). "Diophantine properties of numbers related to Catalan's constant". Mathematische Annalen. 326 (4): 705–721. doi:10.1007/s00208-003-0420-2. hdl:1959.13/803688. ISSN 1432-1807. S2CID 59328860.

springer.com

link.springer.com

Bertrand, Daniel (1997). "Theta functions and transcendence". The Ramanujan Journal. 1 (4): 339–350. doi:10.1023/A:1009749608672. S2CID 118628723.

st-andrews.ac.uk

www-history.mcs.st-andrews.ac.uk

Baker, Alan (1998). J.J. O'Connor and E.F. Robertson. www-history.mcs.st-andrews.ac.uk (biographies). The MacTutor History of Mathematics archive. St. Andrew's, Scotland: University of St. Andrew's.

wikipedia.org

fr.wikipedia.org

Mahler 1929; Allouche & Shallit 2003, p. 387 Mahler, K. (1929). "Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen". Math. Annalen. 101: 342–366. doi:10.1007/bf01454845. JFM 55.0115.01. S2CID 120549929. Allouche, J.-P. [in French]; Shallit, J. (2003). Automatic Sequences: Theory, applications, generalizations. Cambridge University Press. ISBN 978-0-521-82332-6. Zbl 1086.11015.
Allouche & Shallit 2003, pp. 385, 403 Allouche, J.-P. [in French]; Shallit, J. (2003). Automatic Sequences: Theory, applications, generalizations. Cambridge University Press. ISBN 978-0-521-82332-6. Zbl 1086.11015.

wisc.edu

sprott.physics.wisc.edu

Pickover, Cliff. "The 15 most famous transcendental numbers". sprott.physics.wisc.edu. Retrieved 2020-01-23.

wolfram.com

mathworld.wolfram.com

"Weisstein, Eric W. "Liouville's Constant", MathWorld".
Weisstein, Eric W. "Transcendental Number". mathworld.wolfram.com. Retrieved 2023-08-09.
Weisstein, Eric W. "Dottie Number". Wolfram MathWorld. Wolfram Research, Inc. Retrieved 23 July 2016.
Weisstein, Eric W. "Rabbit Constant". mathworld.wolfram.com. Retrieved 2023-08-09.
Weisstein, Eric W. "e". mathworld.wolfram.com. Retrieved 2023-08-12.

worldcat.org

search.worldcat.org

Nesterenko, Yu V (1996-10-31). "Modular functions and transcendence questions". Sbornik: Mathematics. 187 (9): 1319–1348. Bibcode:1996SbMat.187.1319N. doi:10.1070/SM1996v187n09ABEH000158. ISSN 1064-5616.
Lagarias, Jeffrey C. (2013-07-19). "Euler's constant: Euler's work and modern developments". Bulletin of the American Mathematical Society. 50 (4): 527–628. arXiv:1303.1856. doi:10.1090/S0273-0979-2013-01423-X. ISSN 0273-0979.
Adamczewski, Boris; Rivoal, Tanguy (2009). "Irrationality measures for some automatic real numbers". Mathematical Proceedings of the Cambridge Philosophical Society. 147 (3): 659–678. Bibcode:2009MPCPS.147..659A. doi:10.1017/S0305004109002643. ISSN 1469-8064.
Kurosawa, Takeshi (2007-03-01). "Transcendence of certain series involving binary linear recurrences". Journal of Number Theory. 123 (1): 35–58. doi:10.1016/j.jnt.2006.05.019. ISSN 0022-314X.
Duverney, Daniel; Nishioka, Keiji; Nishioka, Kumiko; Shiokawa, Iekata (1997). "Transcendence of Rogers-Ramanujan continued fraction and reciprocal sums of Fibonacci numbers". Proceedings of the Japan Academy, Series A, Mathematical Sciences. 73 (7): 140–142. doi:10.3792/pjaa.73.140. ISSN 0386-2194.
Bailey, David H. (1988). "Numerical Results on the Transcendence of Constants Involving $\pi, e$, and Euler's Constant". Mathematics of Computation. 50 (181): 275–281. doi:10.2307/2007931. ISSN 0025-5718. JSTOR 2007931.
Brownawell, W. Dale (1974-02-01). "The algebraic independence of certain numbers related by the exponential function". Journal of Number Theory. 6 (1): 22–31. Bibcode:1974JNT.....6...22B. doi:10.1016/0022-314X(74)90005-5. ISSN 0022-314X.
Murty, M. Ram; Saradha, N. (2010-12-01). "Euler–Lehmer constants and a conjecture of Erdös". Journal of Number Theory. 130 (12): 2671–2682. doi:10.1016/j.jnt.2010.07.004. ISSN 0022-314X.
Murty, M. Ram; Zaytseva, Anastasia (2013-01-01). "Transcendence of generalized Euler constants". The American Mathematical Monthly. 120 (1): 48–54. doi:10.4169/amer.math.monthly.120.01.048. ISSN 0002-9890. S2CID 20495981.
Rivoal, Tanguy (2012). "On the arithmetic nature of the values of the gamma function, Euler's constant, and Gompertz's constant". Michigan Mathematical Journal. 61 (2): 239–254. doi:10.1307/mmj/1339011525. ISSN 0026-2285.
Rivoal, T.; Zudilin, W. (2003-08-01). "Diophantine properties of numbers related to Catalan's constant". Mathematische Annalen. 326 (4): 705–721. doi:10.1007/s00208-003-0420-2. hdl:1959.13/803688. ISSN 1432-1807. S2CID 59328860.

zbmath.org

Cantor 1874; Gray 1994 Cantor, G. (1874). "Über eine Eigenschaft des Inbegriffes aller reelen algebraischen Zahlen". J. Reine Angew. Math. 77: 258–262. Gray, Robert (1994). "Georg Cantor and transcendental numbers". Amer. Math. Monthly. 101 (9): 819–832. doi:10.2307/2975129. JSTOR 2975129. Zbl 0827.01004 – via maa.org.
Bugeaud 2012, p. 113. Bugeaud, Yann (2012). Distribution modulo one and Diophantine approximation. Cambridge Tracts in Mathematics. Vol. 193. Cambridge University Press. ISBN 978-0-521-11169-0. Zbl 1260.11001.
Pytheas Fogg 2002 Pytheas Fogg, N. (2002). Berthé, V.; Ferenczi, Sébastien; Mauduit, Christian; Siegel, A. (eds.). Substitutions in dynamics, arithmetics and combinatorics. Lecture Notes in Mathematics. Vol. 1794. Springer. ISBN 978-3-540-44141-0. Zbl 1014.11015.
Mahler 1929; Allouche & Shallit 2003, p. 387 Mahler, K. (1929). "Arithmetische Eigenschaften der Lösungen einer Klasse von Funktionalgleichungen". Math. Annalen. 101: 342–366. doi:10.1007/bf01454845. JFM 55.0115.01. S2CID 120549929. Allouche, J.-P. [in French]; Shallit, J. (2003). Automatic Sequences: Theory, applications, generalizations. Cambridge University Press. ISBN 978-0-521-82332-6. Zbl 1086.11015.
Loxton 1988 Loxton, J.H. (1988). "13. Automata and transcendence". In Baker, A. (ed.). New Advances in Transcendence Theory. Cambridge University Press. pp. 215–228. ISBN 978-0-521-33545-4. Zbl 0656.10032.
Allouche & Shallit 2003, pp. 385, 403 Allouche, J.-P. [in French]; Shallit, J. (2003). Automatic Sequences: Theory, applications, generalizations. Cambridge University Press. ISBN 978-0-521-82332-6. Zbl 1086.11015.