Factorial (English Wikipedia)

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

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Datta, Bibhutibhusan; Singh, Awadhesh Narayan (2019). "Use of permutations and combinations in India". In Kolachana, Aditya; Mahesh, K.; Ramasubramanian, K. (eds.). Studies in Indian Mathematics and Astronomy: Selected Articles of Kripa Shankar Shukla. Sources and Studies in the History of Mathematics and Physical Sciences. Springer Singapore. pp. 356–376. doi:10.1007/978-981-13-7326-8_18. ISBN 978-981-13-7325-1. S2CID 191141516.. Revised by K. S. Shukla from a paper in Indian Journal of History of Science 27 (3): 231–249, 1992, MR1189487. See p. 363.
Biggs, Norman L. (May 1979). "The roots of combinatorics". Historia Mathematica. 6 (2): 109–136. doi:10.1016/0315-0860(79)90074-0. MR 0530622.
Rashed, Roshdi (1980). "Ibn al-Haytham et le théorème de Wilson". Archive for History of Exact Sciences (in French). 22 (4): 305–321. doi:10.1007/BF00717654. MR 0595903. S2CID 120885025.
Acerbi, F. (2003). "On the shoulders of Hipparchus: a reappraisal of ancient Greek combinatorics". Archive for History of Exact Sciences. 57 (6): 465–502. doi:10.1007/s00407-003-0067-0. JSTOR 41134173. MR 2004966. S2CID 122758966.
Ebbinghaus, H.-D.; Hermes, H.; Hirzebruch, F.; Koecher, M.; Mainzer, K.; Neukirch, J.; Prestel, A.; Remmert, R. (1990). Numbers. Graduate Texts in Mathematics. Vol. 123. New York: Springer-Verlag. p. 131. doi:10.1007/978-1-4612-1005-4. ISBN 0-387-97202-1. MR 1066206.
Dutka, Jacques (1991). "The early history of the factorial function". Archive for History of Exact Sciences. 43 (3): 225–249. doi:10.1007/BF00389433. JSTOR 41133918. MR 1171521. S2CID 122237769.
Craik, Alex D. D. (2005). "Prehistory of Faà di Bruno's formula". The American Mathematical Monthly. 112 (2): 119–130. doi:10.1080/00029890.2005.11920176. JSTOR 30037410. MR 2121322. S2CID 45380805.
Hamkins, Joel David (2020). Proof and the Art of Mathematics. Cambridge, Massachusetts: MIT Press. p. 50. ISBN 978-0-262-53979-1. MR 4205951.
Riordan, John (1958). An Introduction to Combinatorial Analysis. Wiley Publications in Mathematical Statistics. Chapman & Hall. p. 76. MR 0096594. Reprinted, Princeton Legacy Library, Princeton University Press, 2014, ISBN 9781400854332.
Randić, Milan (1987). "On the evaluation of the characteristic polynomial via symmetric function theory". Journal of Mathematical Chemistry. 1 (1): 145–152. doi:10.1007/BF01205340. MR 0895533. S2CID 121752631.
Hill, Victor E. (2000). "8.1 Proposition: Symmetric group $S n$ ". Groups and Characters. Chapman & Hall. p. 70. ISBN 978-1-351-44381-4. MR 1739394.
Wilf, Herbert S. (2006). generatingfunctionology (3rd ed.). Wellesley, Massachusetts: A K Peters. p. 22. ISBN 978-1-56881-279-3. MR 2172781.
Ore, Øystein (1948). Number Theory and Its History. New York: McGraw-Hill. p. 66. MR 0026059. Reprinted, Courier Dover Publications, 1988, ISBN 9780486656205.
Caldwell, Chris K.; Gallot, Yves (2002). "On the primality of $n!\pm 1$ and $2\times 3\times 5\times \dots \times p\pm 1$ ". Mathematics of Computation. 71 (237): 441–448. doi:10.1090/S0025-5718-01-01315-1. MR 1863013.
Guy, Richard K. (2004). "D25: Equations involving factorial $n$ ". Unsolved Problems in Number Theory. Problem Books in Mathematics. Vol. 1 (3rd ed.). New York: Springer-Verlag. pp. 301–302. doi:10.1007/978-0-387-26677-0. ISBN 0-387-20860-7. MR 2076335.
Chvátal, Vašek (2021). "1.5: Erdős's proof of Bertrand's postulate". The Discrete Mathematical Charms of Paul Erdős: A Simple Introduction. Cambridge, England: Cambridge University Press. pp. 7–10. doi:10.1017/9781108912181. ISBN 978-1-108-83183-3. MR 4282416. S2CID 242637862.
Fraenkel, Aviezri S. (1985). "Systems of numeration". The American Mathematical Monthly. 92 (2): 105–114. doi:10.1080/00029890.1985.11971550. JSTOR 2322638. MR 0777556.
Magnus, Robert (2020). "11.10: Stirling's approximation". Fundamental Mathematical Analysis. Springer Undergraduate Mathematics Series. Cham: Springer. p. 391. doi:10.1007/978-3-030-46321-2. ISBN 978-3-030-46321-2. MR 4178171. S2CID 226465639.
Palmer, Edgar M. (1985). "Appendix II: Stirling's formula". Graphical Evolution: An introduction to the theory of random graphs. Wiley-Interscience Series in Discrete Mathematics. Chichester: John Wiley & Sons. pp. 127–128. ISBN 0-471-81577-2. MR 0795795.
Chen, Chao-Ping; Lin, Long (2012). "Remarks on asymptotic expansions for the gamma function". Applied Mathematics Letters. 25 (12): 2322–2326. doi:10.1016/j.aml.2012.06.025. MR 2967837.
Robert, Alain M. (2000). "3.1: The $p$ -adic valuation of a factorial". A Course in $p$ -adic Analysis. Graduate Texts in Mathematics. Vol. 198. New York: Springer-Verlag. pp. 241–242. doi:10.1007/978-1-4757-3254-2. ISBN 0-387-98669-3. MR 1760253.
Diaconis, Persi (1977). "The distribution of leading digits and uniform distribution mod 1". Annals of Probability. 5 (1): 72–81. doi:10.1214/aop/1176995891. MR 0422186.
Bird, R. S. (1972). "Integers with given initial digits". The American Mathematical Monthly. 79 (4): 367–370. doi:10.1080/00029890.1972.11993051. JSTOR 2978087. MR 0302553.
Luca, Florian (2007). "On factorials which are products of factorials". Mathematical Proceedings of the Cambridge Philosophical Society. 143 (3): 533–542. Bibcode:2007MPCPS.143..533L. doi:10.1017/S0305004107000308. MR 2373957. S2CID 120875316.
Davis, Philip J. (1959). "Leonhard Euler's integral: A historical profile of the gamma function". The American Mathematical Monthly. 66 (10): 849–869. doi:10.1080/00029890.1959.11989422. JSTOR 2309786. MR 0106810. Archived from the original on 2023-01-01. Retrieved 2021-12-20.
Borwein, Jonathan M.; Corless, Robert M. (2018). "Gamma and factorial in the Monthly". The American Mathematical Monthly. 125 (5): 400–424. arXiv:1703.05349. doi:10.1080/00029890.2018.1420983. MR 3785875. S2CID 119324101.
Remmert, Reinhold (1996). "Wielandt's theorem about the $\Gamma$ -function". The American Mathematical Monthly. 103 (3): 214–220. doi:10.1080/00029890.1996.12004726. JSTOR 2975370. MR 1376175.
Alzer, Horst (2009). "A superadditive property of Hadamard's gamma function". Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg. 79 (1): 11–23. doi:10.1007/s12188-008-0009-5. MR 2541340. S2CID 123691692.
Ross, Bertram (1978). "The psi function". Mathematics Magazine. 51 (3): 176–179. doi:10.1080/0025570X.1978.11976704. JSTOR 2689999. MR 1572267.
Borwein, Peter B. (1985). "On the complexity of calculating factorials". Journal of Algorithms. 6 (3): 376–380. doi:10.1016/0196-6774(85)90006-9. MR 0800727.
Harvey, David; van der Hoeven, Joris (2021). "Integer multiplication in time $O(n\log n)$ " (PDF). Annals of Mathematics. Second Series. 193 (2): 563–617. doi:10.4007/annals.2021.193.2.4. MR 4224716. S2CID 109934776.
Meserve, B. E. (1948). "Classroom Notes: Double Factorials". The American Mathematical Monthly. 55 (7): 425–426. doi:10.2307/2306136. JSTOR 2306136. MR 1527019.
Dale, M. R. T.; Moon, J. W. (1993). "The permuted analogues of three Catalan sets". Journal of Statistical Planning and Inference. 34 (1): 75–87. doi:10.1016/0378-3758(93)90035-5. MR 1209991..
Luca, Florian; Marques, Diego (2010). "Perfect powers in the summatory function of the power tower". Journal de Théorie des Nombres de Bordeaux. 22 (3): 703–718. doi:10.5802/jtnb.740. MR 2769339.
Sagan, Bruce E. (2020). "Theorem 1.2.1". Combinatorics: the Art of Counting. Graduate Studies in Mathematics. Vol. 210. Providence, Rhode Island: American Mathematical Society. p. 5. ISBN 978-1-4704-6032-7. MR 4249619.
Daley, D. J.; Vere-Jones, D. (1988). "5.2: Factorial moments, cumulants, and generating function relations for discrete distributions". An Introduction to the Theory of Point Processes. Springer Series in Statistics. New York: Springer-Verlag. p. 112. ISBN 0-387-96666-8. MR 0950166.
Aebi, Christian; Cairns, Grant (2015). "Generalizations of Wilson's theorem for double-, hyper-, sub- and superfactorials". The American Mathematical Monthly. 122 (5): 433–443. doi:10.4169/amer.math.monthly.122.5.433. JSTOR 10.4169/amer.math.monthly.122.5.433. MR 3352802. S2CID 207521192.
Nelson, Randolph (2020). A Brief Journey in Discrete Mathematics. Cham: Springer. p. 127. doi:10.1007/978-3-030-37861-5. ISBN 978-3-030-37861-5. MR 4297795. S2CID 213895324.

archive.org

Dickson, Leonard E. (1919). "Chapter IX: Divisibility of factorials and multinomial coefficients". History of the Theory of Numbers. Vol. 1. Carnegie Institution of Washington. pp. 263–278. See in particular p. 263.
Cajori, Florian (1929). "448–449. Factorial " $n$ "". A History of Mathematical Notations, Volume II: Notations Mainly in Higher Mathematics. The Open Court Publishing Company. pp. 71–77.
Arbogast, Louis François Antoine (1800). Du calcul des dérivations (in French). Strasbourg: L'imprimerie de Levrault, frères. pp. 364–365.
Hardy, G. H. (1921). "Examples XLV". A Course of Pure Mathematics (3rd ed.). Cambridge University Press. p. 215.
Glaisher, J. W. L. (1877). "On the product $11 .2 2 .3 3 ... n n$ ". Messenger of Mathematics. 7: 43–47.

scholar.archive.org

Bhargava, Manjul (2000). "The factorial function and generalizations". The American Mathematical Monthly. 107 (9): 783–799. CiteSeerX 10.1.1.585.2265. doi:10.2307/2695734. JSTOR 2695734.

archives-ouvertes.fr

hal.archives-ouvertes.fr

Harvey, David; van der Hoeven, Joris (2021). "Integer multiplication in time $O(n\log n)$ " (PDF). Annals of Mathematics. Second Series. 193 (2): 563–617. doi:10.4007/annals.2021.193.2.4. MR 4224716. S2CID 109934776.

arxiv.org

Borwein, Jonathan M.; Corless, Robert M. (2018). "Gamma and factorial in the Monthly". The American Mathematical Monthly. 125 (5): 400–424. arXiv:1703.05349. doi:10.1080/00029890.2018.1420983. MR 3785875. S2CID 119324101.
Callan, David (2009). "A combinatorial survey of identities for the double factorial". arXiv:0906.1317 [math.CO].

berkeley.edu

people.eecs.berkeley.edu

Fateman, Richard J. (April 11, 2006). "Comments on Factorial Programs" (PDF). University of California, Berkeley.

books.google.com

Ebbinghaus, H.-D.; Hermes, H.; Hirzebruch, F.; Koecher, M.; Mainzer, K.; Neukirch, J.; Prestel, A.; Remmert, R. (1990). Numbers. Graduate Texts in Mathematics. Vol. 123. New York: Springer-Verlag. p. 131. doi:10.1007/978-1-4612-1005-4. ISBN 0-387-97202-1. MR 1066206.
Hamkins, Joel David (2020). Proof and the Art of Mathematics. Cambridge, Massachusetts: MIT Press. p. 50. ISBN 978-0-262-53979-1. MR 4205951.
Dorf, Richard C. (2003). "Factorials". CRC Handbook of Engineering Tables. CRC Press. p. 5-5. ISBN 978-0-203-00922-2.
Farrell, Orin J.; Ross, Bertram (1971). Solved Problems in Analysis: As Applied to Gamma, Beta, Legendre and Bessel Functions. Dover Books on Mathematics. Courier Corporation. p. 10. ISBN 978-0-486-78308-6.
Riordan, John (1958). An Introduction to Combinatorial Analysis. Wiley Publications in Mathematical Statistics. Chapman & Hall. p. 76. MR 0096594. Reprinted, Princeton Legacy Library, Princeton University Press, 2014, ISBN 9781400854332.
Hill, Victor E. (2000). "8.1 Proposition: Symmetric group $S n$ ". Groups and Characters. Chapman & Hall. p. 70. ISBN 978-1-351-44381-4. MR 1739394.
Christensen, Kim; Moloney, Nicholas R. (2005). "Appendix A: Taylor expansion". Complexity and Criticality. Advanced physics texts. Vol. 1. Imperial College Press. p. 341. ISBN 978-1-86094-504-5.
Wilf, Herbert S. (2006). generatingfunctionology (3rd ed.). Wellesley, Massachusetts: A K Peters. p. 22. ISBN 978-1-56881-279-3. MR 2172781.
Ore, Øystein (1948). Number Theory and Its History. New York: McGraw-Hill. p. 66. MR 0026059. Reprinted, Courier Dover Publications, 1988, ISBN 9780486656205.
Neale, Vicky (2017). Closing the Gap: The Quest to Understand Prime Numbers. Oxford University Press. pp. 146–147. ISBN 978-0-19-878828-7.
Chvátal, Vašek (2021). "1.5: Erdős's proof of Bertrand's postulate". The Discrete Mathematical Charms of Paul Erdős: A Simple Introduction. Cambridge, England: Cambridge University Press. pp. 7–10. doi:10.1017/9781108912181. ISBN 978-1-108-83183-3. MR 4282416. S2CID 242637862.
Knuth, Donald E. (1998). The Art of Computer Programming, Volume 3: Sorting and Searching (2nd ed.). Addison-Wesley. p. 182. ISBN 978-0-321-63578-5.
Sedgewick, Robert; Wayne, Kevin (2011). Algorithms (4th ed.). Addison-Wesley. p. 466. ISBN 978-0-13-276256-4.
Magnus, Robert (2020). "11.10: Stirling's approximation". Fundamental Mathematical Analysis. Springer Undergraduate Mathematics Series. Cham: Springer. p. 391. doi:10.1007/978-3-030-46321-2. ISBN 978-3-030-46321-2. MR 4178171. S2CID 226465639.
Beiler, Albert H. (1966). Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. Dover Recreational Math Series (2nd ed.). Courier Corporation. p. 49. ISBN 978-0-486-21096-4.
Koshy, Thomas (2007). "Example 3.12". Elementary Number Theory with Applications (2nd ed.). Elsevier. p. 178. ISBN 978-0-08-054709-1.
Brase, Charles Henry; Brase, Corrinne Pellillo (2014). Understandable Statistics: Concepts and Methods (11th ed.). Cengage Learning. p. 182. ISBN 978-1-305-14290-9.
Addis, Tom; Addis, Jan (2009). Drawing Programs: The Theory and Practice of Schematic Functional Programming. Springer. pp. 149–150. ISBN 978-1-84882-618-2.
Chapman, Stephen J. (2019). "Example 5.2: The factorial function". MATLAB Programming for Engineers (6th ed.). Cengage Learning. p. 215. ISBN 978-0-357-03052-3.
Hey, Tony; Pápay, Gyuri (2014). The Computing Universe: A Journey through a Revolution. Cambridge University Press. p. 64. ISBN 9781316123225.
Bolboaca, Alexandru (2019). Hands-On Functional Programming with C++: An effective guide to writing accelerated functional code using C++17 and C++20. Packt Publishing. p. 188. ISBN 978-1-78980-921-3.
Gray, John W. (2014). Mastering Mathematica: Programming Methods and Applications. Academic Press. pp. 233–234. ISBN 978-1-4832-1403-0.
Torra, Vicenç (2016). Scala From a Functional Programming Perspective: An Introduction to the Programming Language. Lecture Notes in Computer Science. Vol. 9980. Springer. p. 96. ISBN 978-3-319-46481-7.
Sussman, Gerald Jay (1982). "LISP, programming, and implementation". Functional Programming and Its Applications: An Advanced Course. CREST Advanced Courses. Cambridge University Press. pp. 29–72. ISBN 978-0-521-24503-6. See in particular p. 34.
Sagan, Bruce E. (2020). "Theorem 1.2.1". Combinatorics: the Art of Counting. Graduate Studies in Mathematics. Vol. 210. Providence, Rhode Island: American Mathematical Society. p. 5. ISBN 978-1-4704-6032-7. MR 4249619.
Daley, D. J.; Vere-Jones, D. (1988). "5.2: Factorial moments, cumulants, and generating function relations for discrete distributions". An Introduction to the Theory of Point Processes. Springer Series in Statistics. New York: Springer-Verlag. p. 112. ISBN 0-387-96666-8. MR 0950166.
Nelson, Randolph (2020). A Brief Journey in Discrete Mathematics. Cham: Springer. p. 127. doi:10.1007/978-3-030-37861-5. ISBN 978-3-030-37861-5. MR 4297795. S2CID 213895324.

boost.org

"Factorial". Boost 1.78.0 Documentation: Math Special Functions. Retrieved 2021-12-21.

cedram.org

jtnb.cedram.org

Luca, Florian; Marques, Diego (2010). "Perfect powers in the summatory function of the power tower". Journal de Théorie des Nombres de Bordeaux. 22 (3): 703–718. doi:10.5802/jtnb.740. MR 2769339.

doi.org

Datta, Bibhutibhusan; Singh, Awadhesh Narayan (2019). "Use of permutations and combinations in India". In Kolachana, Aditya; Mahesh, K.; Ramasubramanian, K. (eds.). Studies in Indian Mathematics and Astronomy: Selected Articles of Kripa Shankar Shukla. Sources and Studies in the History of Mathematics and Physical Sciences. Springer Singapore. pp. 356–376. doi:10.1007/978-981-13-7326-8_18. ISBN 978-981-13-7325-1. S2CID 191141516.. Revised by K. S. Shukla from a paper in Indian Journal of History of Science 27 (3): 231–249, 1992, MR1189487. See p. 363.
Jadhav, Dipak (August 2021). "Jaina Thoughts on Unity Not Being a Number". History of Science in South Asia. 9. University of Alberta Libraries: 209–231. doi:10.18732/hssa67. S2CID 238656716.. See discussion of dating on p. 211.
Biggs, Norman L. (May 1979). "The roots of combinatorics". Historia Mathematica. 6 (2): 109–136. doi:10.1016/0315-0860(79)90074-0. MR 0530622.
Rashed, Roshdi (1980). "Ibn al-Haytham et le théorème de Wilson". Archive for History of Exact Sciences (in French). 22 (4): 305–321. doi:10.1007/BF00717654. MR 0595903. S2CID 120885025.
Acerbi, F. (2003). "On the shoulders of Hipparchus: a reappraisal of ancient Greek combinatorics". Archive for History of Exact Sciences. 57 (6): 465–502. doi:10.1007/s00407-003-0067-0. JSTOR 41134173. MR 2004966. S2CID 122758966.
Hunt, Katherine (May 2018). "The Art of Changes: Bell-Ringing, Anagrams, and the Culture of Combination in Seventeenth-Century England" (PDF). Journal of Medieval and Early Modern Studies. 48 (2): 387–412. doi:10.1215/10829636-4403136.
Ebbinghaus, H.-D.; Hermes, H.; Hirzebruch, F.; Koecher, M.; Mainzer, K.; Neukirch, J.; Prestel, A.; Remmert, R. (1990). Numbers. Graduate Texts in Mathematics. Vol. 123. New York: Springer-Verlag. p. 131. doi:10.1007/978-1-4612-1005-4. ISBN 0-387-97202-1. MR 1066206.
Dutka, Jacques (1991). "The early history of the factorial function". Archive for History of Exact Sciences. 43 (3): 225–249. doi:10.1007/BF00389433. JSTOR 41133918. MR 1171521. S2CID 122237769.
Craik, Alex D. D. (2005). "Prehistory of Faà di Bruno's formula". The American Mathematical Monthly. 112 (2): 119–130. doi:10.1080/00029890.2005.11920176. JSTOR 30037410. MR 2121322. S2CID 45380805.
Goldenberg, E. Paul; Carter, Cynthia J. (October 2017). "A student asks about (−5)!". The Mathematics Teacher. 111 (2): 104–110. doi:10.5951/mathteacher.111.2.0104. JSTOR 10.5951/mathteacher.111.2.0104.
Haberman, Bruria; Averbuch, Haim (2002). "The case of base cases: Why are they so difficult to recognize? Student difficulties with recursion". In Caspersen, Michael E.; Joyce, Daniel T.; Goelman, Don; Utting, Ian (eds.). Proceedings of the 7th Annual SIGCSE Conference on Innovation and Technology in Computer Science Education, ITiCSE 2002, Aarhus, Denmark, June 24-28, 2002. Association for Computing Machinery. pp. 84–88. doi:10.1145/544414.544441.
Randić, Milan (1987). "On the evaluation of the characteristic polynomial via symmetric function theory". Journal of Mathematical Chemistry. 1 (1): 145–152. doi:10.1007/BF01205340. MR 0895533. S2CID 121752631.
Caldwell, Chris K.; Gallot, Yves (2002). "On the primality of $n!\pm 1$ and $2\times 3\times 5\times \dots \times p\pm 1$ ". Mathematics of Computation. 71 (237): 441–448. doi:10.1090/S0025-5718-01-01315-1. MR 1863013.
Guy, Richard K. (2004). "D25: Equations involving factorial $n$ ". Unsolved Problems in Number Theory. Problem Books in Mathematics. Vol. 1 (3rd ed.). New York: Springer-Verlag. pp. 301–302. doi:10.1007/978-0-387-26677-0. ISBN 0-387-20860-7. MR 2076335.
Chvátal, Vašek (2021). "1.5: Erdős's proof of Bertrand's postulate". The Discrete Mathematical Charms of Paul Erdős: A Simple Introduction. Cambridge, England: Cambridge University Press. pp. 7–10. doi:10.1017/9781108912181. ISBN 978-1-108-83183-3. MR 4282416. S2CID 242637862.
Fraenkel, Aviezri S. (1985). "Systems of numeration". The American Mathematical Monthly. 92 (2): 105–114. doi:10.1080/00029890.1985.11971550. JSTOR 2322638. MR 0777556.
Pitman, Jim (1993). "3.5: The Poisson distribution". Probability. New York: Springer. pp. 222–236. doi:10.1007/978-1-4612-4374-8. ISBN 978-0-387-94594-1.
Magnus, Robert (2020). "11.10: Stirling's approximation". Fundamental Mathematical Analysis. Springer Undergraduate Mathematics Series. Cham: Springer. p. 391. doi:10.1007/978-3-030-46321-2. ISBN 978-3-030-46321-2. MR 4178171. S2CID 226465639.
Chen, Chao-Ping; Lin, Long (2012). "Remarks on asymptotic expansions for the gamma function". Applied Mathematics Letters. 25 (12): 2322–2326. doi:10.1016/j.aml.2012.06.025. MR 2967837.
Robert, Alain M. (2000). "3.1: The $p$ -adic valuation of a factorial". A Course in $p$ -adic Analysis. Graduate Texts in Mathematics. Vol. 198. New York: Springer-Verlag. pp. 241–242. doi:10.1007/978-1-4757-3254-2. ISBN 0-387-98669-3. MR 1760253.
Peitgen, Heinz-Otto; Jürgens, Hartmut; Saupe, Dietmar (2004). "Kummer's result and Legendre's identity". Chaos and Fractals: New Frontiers of Science. New York: Springer. pp. 399–400. doi:10.1007/b97624. ISBN 978-1-4684-9396-2.
Alladi, Krishnaswami; Grinstead, Charles (1977). "On the decomposition of n! into prime powers". Journal of Number Theory. 9 (4): 452–458. doi:10.1016/0022-314x(77)90006-3.
Diaconis, Persi (1977). "The distribution of leading digits and uniform distribution mod 1". Annals of Probability. 5 (1): 72–81. doi:10.1214/aop/1176995891. MR 0422186.
Bird, R. S. (1972). "Integers with given initial digits". The American Mathematical Monthly. 79 (4): 367–370. doi:10.1080/00029890.1972.11993051. JSTOR 2978087. MR 0302553.
Kempner, A. J. (1918). "Miscellanea". The American Mathematical Monthly. 25 (5): 201–210. doi:10.2307/2972639. JSTOR 2972639.
Erdős, Paul; Kastanas, Ilias (1994). "The smallest factorial that is a multiple of $n$ (solution to problem 6674)" (PDF). The American Mathematical Monthly. 101: 179. doi:10.2307/2324376. JSTOR 2324376..
Bhargava, Manjul (2000). "The factorial function and generalizations". The American Mathematical Monthly. 107 (9): 783–799. CiteSeerX 10.1.1.585.2265. doi:10.2307/2695734. JSTOR 2695734.
Luca, Florian (2007). "On factorials which are products of factorials". Mathematical Proceedings of the Cambridge Philosophical Society. 143 (3): 533–542. Bibcode:2007MPCPS.143..533L. doi:10.1017/S0305004107000308. MR 2373957. S2CID 120875316.
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