Generating function (English Wikipedia)

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

Last modified: 04:49:51, 8 July 2026 (UTC)

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Knuth, D. E. (1992). "Convolution Polynomials". Mathematica J. 2: 67–78. arXiv:math/9207221. Bibcode:1992math......7221K.

ams.org (Global: 434^th place; English: 249^th place)

mathscinet.ams.org

Apostol, Tom M. (1976), Introduction to analytic number theory, Undergraduate Texts in Mathematics, New York-Heidelberg: Springer-Verlag, ISBN 978-0-387-90163-3, MR 0434929, Zbl 0335.10001 pp.42–43
Spivey, Michael Z. (2007). "Combinatorial Sums and Finite Differences". Discrete Math. 307 (24): 3130–3146. doi:10.1016/j.disc.2007.03.052. MR 2370116.

archive.org (Global: 6^th place; English: 6^th place)

Hardy, G.H.; Wright, E.M.; Heath-Brown, D.R; Silverman, J.H. (2008). An Introduction to the Theory of Numbers (6th ed.). Oxford University Press. p. 339. ISBN 9780199219858.

arxiv.org (Global: 49^th place; English: 31^st place)

Knuth, D. E. (1992). "Convolution Polynomials". Mathematica J. 2: 67–78. arXiv:math/9207221. Bibcode:1992math......7221K.
Mathar, R. J. (2012). "Yet another table of integrals". arXiv:1207.5845 [math.CA]. v4 eq. (0.4)
See the following articles:
- Schmidt, Maxie D. (2016). "Continued Fractions for Square Series Generating Functions". arXiv:1612.02778 [math.NT].
- See also the 1031 Generating Functions found in Plouffe, Simon (1992). Approximations de séries génératrices et quelques conjectures [Approximations of generating functions and a few conjectures] (Masters) (in French). Université du Québec à Montréal. arXiv:0911.4975.

books.google.com (Global: 3^rd place; English: 3^rd place)

This alternative term can already be found in E.N. Gilbert (1956), "Enumeration of Labeled graphs", Canadian Journal of Mathematics 3, p. 405–411, but its use is rare before the year 2000; since then it appears to be increasing.
Lando 2003, §2.4 Lando, Sergei K. (2003). Lectures on Generating Functions. American Mathematical Society. ISBN 978-0-8218-3481-7.
Example from Stanley, Richard P.; Fomin, Sergey (1997). "§6.3". Enumerative Combinatorics: Volume 2. Cambridge Studies in Advanced Mathematics. Vol. 62. Cambridge University Press. ISBN 978-0-521-78987-5.
Lando 2003, §5 Lando, Sergei K. (2003). Lectures on Generating Functions. American Mathematical Society. ISBN 978-0-8218-3481-7.

doi.org (Global: 2^nd place; English: 2^nd place)

Spivey, Michael Z. (2007). "Combinatorial Sums and Finite Differences". Discrete Math. 307 (24): 3130–3146. doi:10.1016/j.disc.2007.03.052. MR 2370116.
Good, I. J. (1986). "On applications of symmetric Dirichlet distributions and their mixtures to contingency tables". Annals of Statistics. 4 (6): 1159–1189. doi:10.1214/aos/1176343649.
For more complete information on the properties of J-fractions see:
- Flajolet, P. (1980). "Combinatorial aspects of continued fractions" (PDF). Discrete Mathematics. 32 (2): 125–161. doi:10.1016/0012-365X(80)90050-3.

emis.de (Global: low place; English: low place)

Schneider, C. (2007). "Symbolic Summation Assists Combinatorics". Sém. Lothar. Combin. 56: 1–36.

inria.fr (Global: 6,372^nd place; English: 5,582^nd place)

algo.inria.fr

For more complete information on the properties of J-fractions see:
- Flajolet, P. (1980). "Combinatorial aspects of continued fractions" (PDF). Discrete Mathematics. 32 (2): 125–161. doi:10.1016/0012-365X(80)90050-3.

mathoverflow.net (Global: low place; English: low place)

"Lambert series identity". Math Overflow. 2017.

upenn.edu (Global: 784^th place; English: 498^th place)

math.upenn.edu

Wilf 1994, p. 56 harvnb error: multiple targets (2×): CITEREFWilf1994 (help) Wilf, Herbert S. (1994). Generatingfunctionology (2nd ed.). Academic Press. ISBN 0-12-751956-4. Zbl 0831.05001.
Wilf 1994, p. 59 harvnb error: multiple targets (2×): CITEREFWilf1994 (help) Wilf, Herbert S. (1994). Generatingfunctionology (2nd ed.). Academic Press. ISBN 0-12-751956-4. Zbl 0831.05001.

zbmath.org (Global: 2,089^th place; English: 1,141^st place)

Flajolet & Sedgewick 2009, p. 95 Flajolet, Philippe; Sedgewick, Robert (2009). Analytic Combinatorics. Cambridge University Press. ISBN 978-0-521-89806-5. Zbl 1165.05001.
Apostol, Tom M. (1976), Introduction to analytic number theory, Undergraduate Texts in Mathematics, New York-Heidelberg: Springer-Verlag, ISBN 978-0-387-90163-3, MR 0434929, Zbl 0335.10001 pp.42–43
Wilf 1994, p. 56 harvnb error: multiple targets (2×): CITEREFWilf1994 (help) Wilf, Herbert S. (1994). Generatingfunctionology (2nd ed.). Academic Press. ISBN 0-12-751956-4. Zbl 0831.05001.
Wilf 1994, p. 59 harvnb error: multiple targets (2×): CITEREFWilf1994 (help) Wilf, Herbert S. (1994). Generatingfunctionology (2nd ed.). Academic Press. ISBN 0-12-751956-4. Zbl 0831.05001.
Graham, Knuth & Patashnik 1994, Table 265 in §6.1 for finite sum identities involving the Stirling number triangles. Graham, Ronald L.; Knuth, Donald E.; Patashnik, Oren (1994). "Chapter 7: Generating Functions". Concrete Mathematics. A foundation for computer science (2nd ed.). Addison-Wesley. pp. 320–380. ISBN 0-201-55802-5. Zbl 0836.00001.
Solution to Graham, Knuth & Patashnik 1994, p. 569, exercise 7.36 Graham, Ronald L.; Knuth, Donald E.; Patashnik, Oren (1994). "Chapter 7: Generating Functions". Concrete Mathematics. A foundation for computer science (2nd ed.). Addison-Wesley. pp. 320–380. ISBN 0-201-55802-5. Zbl 0836.00001.
Flajolet & Sedgewick 2009, §B.4 Flajolet, Philippe; Sedgewick, Robert (2009). Analytic Combinatorics. Cambridge University Press. ISBN 978-0-521-89806-5. Zbl 1165.05001.
See the usage of these terms in Graham, Knuth & Patashnik 1994, §7.4 on special sequence generating functions. Graham, Ronald L.; Knuth, Donald E.; Patashnik, Oren (1994). "Chapter 7: Generating Functions". Concrete Mathematics. A foundation for computer science (2nd ed.). Addison-Wesley. pp. 320–380. ISBN 0-201-55802-5. Zbl 0836.00001.
Graham, Knuth & Patashnik 1994, §8.3 Graham, Ronald L.; Knuth, Donald E.; Patashnik, Oren (1994). "Chapter 7: Generating Functions". Concrete Mathematics. A foundation for computer science (2nd ed.). Addison-Wesley. pp. 320–380. ISBN 0-201-55802-5. Zbl 0836.00001.
Graham, Knuth & Patashnik 1994, Example 6 in §7.3 for another method and the complete setup of this problem using generating functions. This more "convoluted" approach is given in Section 7.5 of the same reference. Graham, Ronald L.; Knuth, Donald E.; Patashnik, Oren (1994). "Chapter 7: Generating Functions". Concrete Mathematics. A foundation for computer science (2nd ed.). Addison-Wesley. pp. 320–380. ISBN 0-201-55802-5. Zbl 0836.00001.
Graham, Knuth & Patashnik 1994, p. 535, exercise 5.71 Graham, Ronald L.; Knuth, Donald E.; Patashnik, Oren (1994). "Chapter 7: Generating Functions". Concrete Mathematics. A foundation for computer science (2nd ed.). Addison-Wesley. pp. 320–380. ISBN 0-201-55802-5. Zbl 0836.00001.

Generating function (English Wikipedia)

adsabs.harvard.edu (Global: 14th place; English: 9th place)

ui.adsabs.harvard.edu

ams.org (Global: 434th place; English: 249th place)

mathscinet.ams.org

archive.org (Global: 6th place; English: 6th place)

arxiv.org (Global: 49th place; English: 31st place)

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doi.org (Global: 2nd place; English: 2nd place)