Superfunction/Bibliography: Difference between revisions
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==About superfactorial and <math> \sqrt{!} </math>== | |||
About <math>\sqrt{!}</math> as logo | |||
About <math>\sqrt{!}</math> | |||
<ref name="logo">Logo of the Physics Department of the Moscow State University. (In Russian); | <ref name="logo">Logo of the Physics Department of the Moscow State University. (In Russian); | ||
http://zhurnal.lib.ru/img/g/garik/dubinushka/index.shtml | http://zhurnal.lib.ru/img/g/garik/dubinushka/index.shtml | ||
| Line 30: | Line 30: | ||
About superfactorial and <math> \sqrt{!} </math>: | About superfactorial and <math> \sqrt{!} </math>: | ||
<ref name="superfactorial"> | <ref name="superfactorial"> | ||
D.Kouznetsov, H.Trappmann. Superfunctions and square root of factorial. Preprint ILS, 2009: | D.Kouznetsov, H.Trappmann. Superfunctions and square root of factorial. Preprint ILS UEC, 2009: | ||
http://www.ils.uec.ac.jp/~dima/PAPERS/2009supefae.pdf | http://www.ils.uec.ac.jp/~dima/PAPERS/2009supefae.pdf | ||
</ref> | </ref> | ||
| Line 38: | Line 38: | ||
Tetration for base <math>b\!=\!\mathrm{e}</math> | Tetration for base <math>b\!=\!\mathrm{e}</math> | ||
<ref name="kneser"> | <ref name="kneser"> | ||
H.Kneser. “Reelle analytische L¨osungen der Gleichung | H.Kneser. “Reelle analytische L¨osungen der Gleichung | ||
<math>\varphi(\varphi(x)) = \exp(x)</math> und verwandter Funktionalgleichungen”. | |||
Journal f¨ur die reine und angewandte Mathematik, 187 (1950), 56-67. | Journal f¨ur die reine und angewandte Mathematik, 187 (1950), 56-67. | ||
</ref> | </ref> | ||
| Line 68: | Line 69: | ||
Linear and piece-vice approximation of tetration | Linear and piece-vice approximation of tetration | ||
<ref name="uxp"> | <ref name="uxp"> | ||
{{cite | {{cite journal | ||
|author=M.H.Hooshmand | |author=M.H.Hooshmand | ||
|title=Ultra power and ultra exponential functions | |title=Ultra power and ultra exponential functions | ||
| Line 79: | Line 80: | ||
</ref> | </ref> | ||
Application of tetration <ref> | Application of tetration <ref>P.Walker. Infinitely differentiable generalized logarithmic and exponential functions. Mathematics | ||
P.Walker. Infinitely differentiable generalized logarithmic and exponential functions. Mathematics | |||
of computation, 196 (1991), 723-733. | of computation, 196 (1991), 723-733. | ||
</ref> | </ref> | ||
<ref name="uxp" | <ref name="uxp"/> | ||
<ref name="a"> W.Ackermann. ”Zum Hilbertschen Aufbau der reellen Zahlen”. Mathematische Annalen | <ref name="a"> W.Ackermann. ”Zum Hilbertschen Aufbau der reellen Zahlen”. Mathematische Annalen | ||
99(1928), 118-133</ref> | 99(1928), 118-133</ref> | ||
<ref name="k2" | <ref name="k2"/>. | ||
==Additional literature around== | ==Additional literature around== | ||
| Line 108: | Line 96: | ||
99(1928), 118-133</ref> | 99(1928), 118-133</ref> | ||
==References== | |||
<small> | |||
<references> | |||
<references/> | </references> | ||
</small> | |||
Latest revision as of 14:01, 9 November 2024
- Please sort and annotate in a user-friendly manner. For formatting, consider using automated reference wikification.
About superfactorial and
About superfactorial and : [4]
About superexponentias and
Tetrational to base [7].
Superexponentials (and, in particular the tetrational) to base [8]
Linear and piece-vice approximation of tetration [9]
Application of tetration [10] [9] [11] [7].
Additional literature around
Reiterated exponential [12].
Ackermann Function [11]
References
- ↑ Logo of the Physics Department of the Moscow State University. (In Russian); http://zhurnal.lib.ru/img/g/garik/dubinushka/index.shtml
- ↑
V.P.Kandidov. About the time and myself. (In Russian)
http://ofvp.phys.msu.ru/pdf/Kandidov_70.pdf:
По итогам студенческого голосования победителями оказались значок с изображением
рычага, поднимающего Землю, и нынешний с хорошо известной эмблемой в виде корня из факториала, вписанными в букву Ф. Этот значок, созданный студентом кафедры биофизики А.Сарвазяном, привлекал своей простотой и выразительностью. Тогда эмблема этого значка подверглась жесткой критике со стороны руководства факультета, поскольку она не имеет физического смысла, математически абсурдна и идеологически бессодержательна.
- ↑
250 anniversary of the Moscow State University. (In Russian)
ПЕРВОМУ УНИВЕРСИТЕТУ СТРАНЫ - 250!
http://nauka.relis.ru/11/0412/11412002.htm
На значке физфака в букву "Ф" вписано стилизованное изображение корня из факториала (√!) - выражение, математического смысла не имеющее.
- ↑ D.Kouznetsov, H.Trappmann. Superfunctions and square root of factorial. Preprint ILS UEC, 2009: http://www.ils.uec.ac.jp/~dima/PAPERS/2009supefae.pdf
- ↑ H.Kneser. “Reelle analytische L¨osungen der Gleichung und verwandter Funktionalgleichungen”. Journal f¨ur die reine und angewandte Mathematik, 187 (1950), 56-67.
- ↑ D.Kouznetsov (2008). "Solutions of in the complex plane.". Mathematics of Computation 78: 1647-1670. DOI:10.1090/S0025-5718-09-02188-7. Research Blogging.
- ↑ 7.0 7.1 D.Kouznetsov. Ackermann functions of complex argument. Preprint ILS UEC, 2008. http://www.ils.uec.ac.jp/~dima/PAPERS/2008ackermann.pdf
- ↑ D.Kouznetsov, H.Trappmann. Portrait of the four regular super-exponentials to base sqrt(2). Preprint ILS UEC, http://www.ils.uec.ac.jp/~dima/PAPERS/2009sqrt2.pdf
- ↑ 9.0 9.1 M.H.Hooshmand (2006). "Ultra power and ultra exponential functions". Integral Transforms and Special Functions 17 (8): 549-558.
- ↑ P.Walker. Infinitely differentiable generalized logarithmic and exponential functions. Mathematics of computation, 196 (1991), 723-733.
- ↑ 11.0 11.1 W.Ackermann. ”Zum Hilbertschen Aufbau der reellen Zahlen”. Mathematische Annalen 99(1928), 118-133
- ↑ A.Knoebel. ”Exponentials Reiterated.” Amer. Math. Monthly 88 (1981), 235-252.
