क्रमगुणित (Hindi Wikipedia)

Analysis of information sources in references of the Wikipedia article "क्रमगुणित" in Hindi language version.

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Biggs, Norman L. (May 1979). "The roots of combinatorics". Historia Mathematica. 6 (2): 109–136. MR 0530622. डीओआइ:10.1016/0315-0860(79)90074-0.
Rashed, Roshdi (1980). "Ibn al-Haytham et le théorème de Wilson". Archive for History of Exact Sciences (फ़्रेंच में). 22 (4): 305–321. MR 0595903. S2CID 120885025. डीओआइ:10.1007/BF00717654.
Acerbi, F. (2003). "On the shoulders of Hipparchus: a reappraisal of ancient Greek combinatorics". Archive for History of Exact Sciences. 57 (6): 465–502. JSTOR 41134173. MR 2004966. S2CID 122758966. डीओआइ:10.1007/s00407-003-0067-0.
Ebbinghaus, H.-D.; Hermes, H.; Hirzebruch, F.; Koecher, M.; Mainzer, K.; Neukirch, J.; Prestel, A.; Remmert, R. (1990). Numbers. Graduate Texts in Mathematics. 123. New York: Springer-Verlag. पृ॰ 131. MR 1066206. आई॰ऍस॰बी॰ऍन॰ 0-387-97202-1. डीओआइ:10.1007/978-1-4612-1005-4.
Dutka, Jacques (1991). "क्रमगुणित फलन का प्रारंभिक इतिहास". Archive for History of Exact Sciences. 43 (3): 225–249. JSTOR 41133918. MR 1171521. S2CID 122237769. डीओआइ:10.1007/BF00389433.
Craik, Alex D. D. (2005). "Prehistory of Faà di Bruno's formula". The American Mathematical Monthly. 112 (2): 119–130. JSTOR 30037410. MR 2121322. S2CID 45380805. डीओआइ:10.1080/00029890.2005.11920176.
हैमकिंस, जोएल डेविड (2020). प्रमाण और गणित की कला. कैम्ब्रिज, मैसाचुसेट्स: एमआईटी प्रेस. पृ॰ 50. MR 4205951. आई॰ऍस॰बी॰ऍन॰ 978-0-262-53979-1.
Riordan, John (1958). An Introduction to Combinatorial Analysis. Wiley Publications in Mathematical Statistics. Chapman & Hall. पृ॰ 76. MR 0096594. आई॰ऍस॰बी॰ऍन॰ 9781400854332.
Randić, Milan (1987). "On the evaluation of the characteristic polynomial via symmetric function theory". Journal of Mathematical Chemistry. 1 (1): 145–152. MR 0895533. S2CID 121752631. डीओआइ:10.1007/BF01205340.
Hill, Victor E. (2000). "8.1 Proposition: Symmetric group $S n$ ". Groups and Characters. Chapman & Hall. पृ॰ 70. MR 1739394. आई॰ऍस॰बी॰ऍन॰ 978-1-351-44381-4.
Wilf, Herbert S. (2006). generatingfunctionology (3rd संस्करण). Wellesley, Massachusetts: A K Peters. पृ॰ 22. MR 2172781. आई॰ऍस॰बी॰ऍन॰ 978-1-56881-279-3.
Ore, Øystein (1948). Number Theory and Its History. New York: McGraw-Hill. पृ॰ 66. MR 0026059. आई॰ऍस॰बी॰ऍन॰ 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. MR 1863013. डीओआइ:10.1090/S0025-5718-01-01315-1.
Guy, Richard K. (2004). "D25: Equations involving factorial $n$ ". Unsolved Problems in Number Theory. Problem Books in Mathematics. 1 (3rd संस्करण). New York: Springer-Verlag. पपृ॰ 301–302. MR 2076335. आई॰ऍस॰बी॰ऍन॰ 0-387-20860-7. डीओआइ:10.1007/978-0-387-26677-0.
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. पपृ॰ 7–10. MR 4282416. S2CID 242637862. आई॰ऍस॰बी॰ऍन॰ 978-1-108-83183-3. डीओआइ:10.1017/9781108912181.
Fraenkel, Aviezri S. (1985). "Systems of numeration". The American Mathematical Monthly. 92 (2): 105–114. JSTOR 2322638. MR 0777556. डीओआइ:10.1080/00029890.1985.11971550.
Magnus, Robert (2020). "11.10: Stirling's approximation". मौलिक गणितीय विश्लेषण. Springer Undergraduate Mathematics Series. Cham: Springer. पृ॰ 391. MR 4178171. S2CID 226465639. आई॰ऍस॰बी॰ऍन॰ 978-3-030-46321-2. डीओआइ:10.1007/978-3-030-46321-2.
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. पपृ॰ 127–128. MR 0795795. आई॰ऍस॰बी॰ऍन॰ 0-471-81577-2.
Chen, Chao-Ping; Lin, Long (2012). "Remarks on asymptotic expansions for the gamma function". Applied Mathematics Letters. 25 (12): 2322–2326. MR 2967837. डीओआइ:10.1016/j.aml.2012.06.025.
Robert, Alain M. (2000). "3.1: The $p$ -adic valuation of a factorial". A Course in $p$ -adic Analysis. Graduate Texts in Mathematics. 198. New York: Springer-Verlag. पपृ॰ 241–242. MR 1760253. आई॰ऍस॰बी॰ऍन॰ 0-387-98669-3. डीओआइ:10.1007/978-1-4757-3254-2.
Diaconis, Persi (1977). "The distribution of leading digits and uniform distribution mod 1". Annals of Probability. 5 (1): 72–81. MR 0422186. डीओआइ:10.1214/aop/1176995891.
Bird, R. S. (1972). "Integers with given initial digits". The American Mathematical Monthly. 79 (4): 367–370. JSTOR 2978087. MR 0302553. डीओआइ:10.1080/00029890.1972.11993051.
Luca, Florian (2007). "On factorials which are products of factorials". Mathematical Proceedings of the Cambridge Philosophical Society. 143 (3): 533–542. MR 2373957. S2CID 120875316. डीओआइ:10.1017/S0305004107000308. बिबकोड:2007MPCPS.143..533L.
Davis, Philip J. (1959). "Leonhard Euler's integral: A historical profile of the gamma function". The American Mathematical Monthly. 66 (10): 849–869. JSTOR 2309786. MR 0106810. डीओआइ:10.1080/00029890.1959.11989422. मूल से 1 जनवरी 2023 को पुरालेखित. अभिगमन तिथि 9 जून 2024.
Borwein, Jonathan M.; Corless, Robert M. (2018). "Gamma and factorial in the Monthly". The American Mathematical Monthly. 125 (5): 400–424. arXiv:1703.05349. MR 3785875. S2CID 119324101. डीओआइ:10.1080/00029890.2018.1420983.
Remmert, Reinhold (1996). "Wielandt's theorem about the $\Gamma$ -function". The American Mathematical Monthly. 103 (3): 214–220. JSTOR 2975370. MR 1376175. डीओआइ:10.1080/00029890.1996.12004726.
Alzer, Horst (2009). "A superadditive property of Hadamard's gamma function". Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg. 79 (1): 11–23. MR 2541340. S2CID 123691692. डीओआइ:10.1007/s12188-008-0009-5.
Ross, Bertram (1978). "The psi function". Mathematics Magazine. 51 (3): 176–179. JSTOR 2689999. MR 1572267. डीओआइ:10.1080/0025570X.1978.11976704.
Borwein, Peter B. (1985). "On the complexity of calculating factorials". Journal of Algorithms. 6 (3): 376–380. MR 0800727. डीओआइ:10.1016/0196-6774(85)90006-9.
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. MR 4224716. S2CID 109934776. डीओआइ:10.4007/annals.2021.193.2.4.
Meserve, B. E. (1948). "Classroom Notes: Double Factorials". The American Mathematical Monthly. 55 (7): 425–426. JSTOR 2306136. MR 1527019. डीओआइ:10.2307/2306136.
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. MR 1209991. डीओआइ:10.1016/0378-3758(93)90035-5..
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. MR 2769339. डीओआइ:10.5802/jtnb.740.
Sagan, Bruce E. (2020). "Theorem 1.2.1". Combinatorics: the Art of Counting. Graduate Studies in Mathematics. 210. Providence, Rhode Island: American Mathematical Society. पृ॰ 5. MR 4249619. आई॰ऍस॰बी॰ऍन॰ 978-1-4704-6032-7.
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. पृ॰ 112. MR 0950166. आई॰ऍस॰बी॰ऍन॰ 0-387-96666-8.
Aebi, Christian; Cairns, Grant (2015). "Generalizations of Wilson's theorem for double-, hyper-, sub- and superfactorials". The American Mathematical Monthly. 122 (5): 433–443. JSTOR 10.4169/amer.math.monthly.122.5.433. MR 3352802. S2CID 207521192. डीओआइ:10.4169/amer.math.monthly.122.5.433.
Nelson, Randolph (2020). A Brief Journey in Discrete Mathematics. Cham: Springer. पृ॰ 127. MR 4297795. S2CID 213895324. आई॰ऍस॰बी॰ऍन॰ 978-3-030-37861-5. डीओआइ:10.1007/978-3-030-37861-5.

archive.org

Rashed, Roshdi (1980). "Ibn al-Haytham et le théorème de Wilson". Archive for History of Exact Sciences (फ़्रेंच में). 22 (4): 305–321. MR 0595903. S2CID 120885025. डीओआइ:10.1007/BF00717654.
Katz, Victor J. (2013). "Chapter 4: Jewish combinatorics". प्रकाशित Wilson, Robin; Watkins, John J. (संपा॰). Combinatorics: Ancient & Modern. Oxford University Press. पपृ॰ 109–121. आई॰ऍस॰बी॰ऍन॰ 978-0-19-965659-2. पृष्ठ 111 देखें।
Stedman, Fabian (1677). Campanalogia. London. पपृ॰ 6–9. The publisher is given as "W.S." who may have been William Smith, possibly acting as agent for the Society of College Youths, to which society the "Dedicatory" is addressed.
Knobloch, Eberhard (2013). "Chapter 5: Renaissance combinatorics". प्रकाशित Wilson, Robin; Watkins, John J. (संपा॰). Combinatorics: Ancient & Modern. Oxford University Press. पपृ॰ 123–145. आई॰ऍस॰बी॰ऍन॰ 978-0-19-965659-2. पृष्ठ 126 देखें।
Dutka, Jacques (1991). "क्रमगुणित फलन का प्रारंभिक इतिहास". Archive for History of Exact Sciences. 43 (3): 225–249. JSTOR 41133918. MR 1171521. S2CID 122237769. डीओआइ:10.1007/BF00389433.
Dickson, Leonard E. (1919). "Chapter IX: Divisibility of factorials and multinomial coefficients". History of the Theory of Numbers. 1. Carnegie Institution of Washington. पपृ॰ 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. पपृ॰ 71–77.
Craik, Alex D. D. (2005). "Prehistory of Faà di Bruno's formula". The American Mathematical Monthly. 112 (2): 119–130. JSTOR 30037410. MR 2121322. S2CID 45380805. डीओआइ:10.1080/00029890.2005.11920176.
Arbogast, Louis François Antoine (1800). Du calcul des dérivations (फ़्रेंच में). Strasbourg: L'imprimerie de Levrault, frères. पपृ॰ 364–365.
Arbogast, Louis François Antoine (1800). Du calcul des dérivations (फ़्रेंच में). Strasbourg: L'imprimerie de Levrault, frères. पपृ॰ 364–365.
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. MR 1863013. डीओआइ:10.1090/S0025-5718-01-01315-1.
Fraenkel, Aviezri S. (1985). "Systems of numeration". The American Mathematical Monthly. 92 (2): 105–114. JSTOR 2322638. MR 0777556. डीओआइ:10.1080/00029890.1985.11971550.
Diaconis, Persi (1977). "The distribution of leading digits and uniform distribution mod 1". Annals of Probability. 5 (1): 72–81. MR 0422186. डीओआइ:10.1214/aop/1176995891.
Bird, R. S. (1972). "Integers with given initial digits". The American Mathematical Monthly. 79 (4): 367–370. JSTOR 2978087. MR 0302553. डीओआइ:10.1080/00029890.1972.11993051.
Kempner, A. J. (1918). "Miscellanea". The American Mathematical Monthly. 25 (5): 201–210. JSTOR 2972639. डीओआइ:10.2307/2972639.
Remmert, Reinhold (1996). "Wielandt's theorem about the $\Gamma$ -function". The American Mathematical Monthly. 103 (3): 214–220. JSTOR 2975370. MR 1376175. डीओआइ:10.1080/00029890.1996.12004726.
Ross, Bertram (1978). "The psi function". Mathematics Magazine. 51 (3): 176–179. JSTOR 2689999. MR 1572267. डीओआइ:10.1080/0025570X.1978.11976704.
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. MR 1209991. डीओआइ:10.1016/0378-3758(93)90035-5..
Hardy, G. H. (1921). "Examples XLV". A Course of Pure Mathematics (3rd संस्करण). Cambridge University Press. पृ॰ 215.
Glaisher, J. W. L. (1877). "On the product $11 .2 2 .3 3 ... n n$ ". Messenger of Mathematics. 7: 43–47.
Aebi, Christian; Cairns, Grant (2015). "Generalizations of Wilson's theorem for double-, hyper-, sub- and superfactorials". The American Mathematical Monthly. 122 (5): 433–443. JSTOR 10.4169/amer.math.monthly.122.5.433. MR 3352802. S2CID 207521192. डीओआइ:10.4169/amer.math.monthly.122.5.433.

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. MR 4224716. S2CID 109934776. डीओआइ:10.4007/annals.2021.193.2.4.

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. MR 3785875. S2CID 119324101. डीओआइ:10.1080/00029890.2018.1420983.
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. 123. New York: Springer-Verlag. पृ॰ 131. MR 1066206. आई॰ऍस॰बी॰ऍन॰ 0-387-97202-1. डीओआइ:10.1007/978-1-4612-1005-4.
हैमकिंस, जोएल डेविड (2020). प्रमाण और गणित की कला. कैम्ब्रिज, मैसाचुसेट्स: एमआईटी प्रेस. पृ॰ 50. MR 4205951. आई॰ऍस॰बी॰ऍन॰ 978-0-262-53979-1.
Dorf, Richard C. (2003). "Factorials". CRC Handbook of Engineering Tables. CRC Press. पृ॰ 5-5. आई॰ऍस॰बी॰ऍन॰ 978-0-203-00922-2.
फैरेल, ओरिन जे.; रॉस, बर्ट्रम (1971). विश्लेषण में हल की गई समस्याएं: जैसा कि गामा, बीटा, लीजेंड्रे और बेसेल फ़ंक्शन पर लागू होता है. डोवर बुक्स ऑन मैथमेटिक्स. कूरियर कॉर्पोरेशन. पृ॰ 10. आई॰ऍस॰बी॰ऍन॰ 978-0-486-78308-6.
Riordan, John (1958). An Introduction to Combinatorial Analysis. Wiley Publications in Mathematical Statistics. Chapman & Hall. पृ॰ 76. MR 0096594. आई॰ऍस॰बी॰ऍन॰ 9781400854332.
Hill, Victor E. (2000). "8.1 Proposition: Symmetric group $S n$ ". Groups and Characters. Chapman & Hall. पृ॰ 70. MR 1739394. आई॰ऍस॰बी॰ऍन॰ 978-1-351-44381-4.
Christensen, Kim; Moloney, Nicholas R. (2005). "Appendix A: Taylor expansion". Complexity and Criticality. Advanced physics texts. 1. Imperial College Press. पृ॰ 341. आई॰ऍस॰बी॰ऍन॰ 978-1-86094-504-5.
Wilf, Herbert S. (2006). generatingfunctionology (3rd संस्करण). Wellesley, Massachusetts: A K Peters. पृ॰ 22. MR 2172781. आई॰ऍस॰बी॰ऍन॰ 978-1-56881-279-3.
Ore, Øystein (1948). Number Theory and Its History. New York: McGraw-Hill. पृ॰ 66. MR 0026059. आई॰ऍस॰बी॰ऍन॰ 9780486656205.
Neale, Vicky (2017). Closing the Gap: The Quest to Understand Prime Numbers. Oxford University Press. पपृ॰ 146–147. आई॰ऍस॰बी॰ऍन॰ 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. पपृ॰ 7–10. MR 4282416. S2CID 242637862. आई॰ऍस॰बी॰ऍन॰ 978-1-108-83183-3. डीओआइ:10.1017/9781108912181.
Knuth, Donald E. (1998). द आर्ट ऑफ कंप्यूटर प्रोग्रामिंग, खंड 3: सॉर्टिंग एंड सर्चिंग (2nd संस्करण). Addison-Wesley. पृ॰ 182. आई॰ऍस॰बी॰ऍन॰ 978-0-321-63578-5.
Sedgewick, Robert; Wayne, Kevin (2011). Algorithms (4th संस्करण). Addison-Wesley. पृ॰ 466. आई॰ऍस॰बी॰ऍन॰ 978-0-13-276256-4.
Magnus, Robert (2020). "11.10: Stirling's approximation". मौलिक गणितीय विश्लेषण. Springer Undergraduate Mathematics Series. Cham: Springer. पृ॰ 391. MR 4178171. S2CID 226465639. आई॰ऍस॰बी॰ऍन॰ 978-3-030-46321-2. डीओआइ:10.1007/978-3-030-46321-2.
Beiler, Albert H. (1966). Recreations in the Theory of Numbers: The Queen of Mathematics Entertains. Dover Recreational Math Series (2nd संस्करण). Courier Corporation. पृ॰ 49. आई॰ऍस॰बी॰ऍन॰ 978-0-486-21096-4.
Koshy, Thomas (2007). "Example 3.12". Elementary Number Theory with Applications (2nd संस्करण). Elsevier. पृ॰ 178. आई॰ऍस॰बी॰ऍन॰ 978-0-08-054709-1.
Brase, Charles Henry; Brase, Corrinne Pellillo (2014). Understandable Statistics: Concepts and Methods (11th संस्करण). Cengage Learning. पृ॰ 182. आई॰ऍस॰बी॰ऍन॰ 978-1-305-14290-9.
Addis, Tom; Addis, Jan (2009). Drawing Programs: The Theory and Practice of Schematic Functional Programming. Springer. पपृ॰ 149–150. आई॰ऍस॰बी॰ऍन॰ 978-1-84882-618-2.
Chapman, Stephen J. (2019). "Example 5.2: The factorial function". MATLAB Programming for Engineers (6th संस्करण). Cengage Learning. पृ॰ 215. आई॰ऍस॰बी॰ऍन॰ 978-0-357-03052-3.
Hey, Tony; Pápay, Gyuri (2014). The Computing Universe: A Journey through a Revolution. Cambridge University Press. पृ॰ 64. आई॰ऍस॰बी॰ऍन॰ 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. पृ॰ 188. आई॰ऍस॰बी॰ऍन॰ 978-1-78980-921-3.
Gray, John W. (2014). Mastering Mathematica: Programming Methods and Applications. Academic Press. पपृ॰ 233–234. आई॰ऍस॰बी॰ऍन॰ 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. 9980. Springer. पृ॰ 96. आई॰ऍस॰बी॰ऍन॰ 978-3-319-46481-7.
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