Superfunction/Bibliography: Difference between revisions
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==About superfunctions of factorial and <math> \sqrt{!} </math> | |||
About <math>\sqrt{!}</math> | 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 | ||
</ref><ref name=" | </ref> | ||
==About superfunctions of exponentias and <math> \sqrt{\exp} </math>== | |||
Tetration for base <math>b\!=\!\mathrm{e}</math> | |||
<ref name="kneser"> | |||
H.Kneser. “Reelle analytische L¨osungen der Gleichung '('(x)) = ex und verwandter Funktionalgleichungen”. | |||
Journal f¨ur die reine und angewandte Mathematik, 187 (1950), 56-67. | |||
</ref> | |||
<ref name="k">D.Kouznetsov. Solutions of <math>F(z+1)=\exp(F(z))</math> in the complex <math>z</math>plane. [[Mathematics of Computation]], 2008, in press; preprint: http://www.ils.uec.ac.jp/~dima/PAPERS/analuxp99.pdf</ref> | |||
Tetration for base <math>b\!=\!2</math> | |||
<ref name="k2">D.Kouznetsov. Ackermann functions of complex argument. Preprint of the Institute for Laser Science, UEC, 2008. | |||
http://www.ils.uec.ac.jp/~dima/PAPERS/2008ackermann.pdf</ref>. | |||
Linear and piece-vice approximation of tetration | |||
<ref name="uxp"> | |||
M.H.Hooshmand. ”Ultra power and ultra exponential functions”. Integral Transforms and | |||
Special Functions 17 (8), 549-558 (2006)</ref> | |||
Application of tetration <ref> | |||
P.Walker. Infinitely differentiable generalized logarithmic and exponential functions. Mathematics | |||
of computation, 196 (1991), 723-733. | |||
</ref> | |||
<ref name="uxp"> | |||
M.H.Hooshmand. ”Ultra power and ultra exponential functions”. Integral Transforms and | |||
Special Functions 17 (8), 549-558 (2006) | |||
</ref> | |||
<ref name="a"> W.Ackermann. ”Zum Hilbertschen Aufbau der reellen Zahlen”. Mathematische Annalen | |||
99(1928), 118-133</ref> | |||
<ref name="k2"> | |||
D.Kouznetsov. Ackermann functions of complex argument. In preparation; | |||
Preprint: http://www.ils.uec.ac.jp/~dima/PAPERS/2008ackermann.pdf | |||
</ref>. | |||
<ref name="k2"> | |||
D.Kouznetsov. Ackermann functions of complex argument. In preparation; | |||
Preprint: http://www.ils.uec.ac.jp/~dima/PAPERS/2008ackermann.pdf | |||
</ref>. | |||
==Additional literature around== | |||
Reiterated exponential | |||
<ref>A.Knoebel. ”Exponentials Reiterated.” Amer. Math. Monthly 88 (1981), 235-252.</ref>. | |||
Ackermann Function | |||
<ref name="a"> W.Ackermann. ”Zum Hilbertschen Aufbau der reellen Zahlen”. Mathematische Annalen | |||
99(1928), 118-133</ref> | |||
<references/> | <references/> | ||
Revision as of 02:03, 14 August 2009
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==About superfunctions of factorial and
About [1]
About superfunctions of exponentias and
Tetration for base [4].
Linear and piece-vice approximation of tetration [5]
Application of tetration [6] [5] [7] [4].
[4].
Additional literature around
Reiterated exponential [8].
Ackermann Function [7]
- ↑ Logo of the Physics Department of the Moscow State University. (In Russian); http://zhurnal.lib.ru/img/g/garik/dubinushka/index.shtml
- ↑ H.Kneser. “Reelle analytische L¨osungen der Gleichung '('(x)) = ex und verwandter Funktionalgleichungen”. Journal f¨ur die reine und angewandte Mathematik, 187 (1950), 56-67.
- ↑ D.Kouznetsov. Solutions of in the complex plane. Mathematics of Computation, 2008, in press; preprint: http://www.ils.uec.ac.jp/~dima/PAPERS/analuxp99.pdf
- ↑ 4.0 4.1 4.2 D.Kouznetsov. Ackermann functions of complex argument. Preprint of the Institute for Laser Science, UEC, 2008.
http://www.ils.uec.ac.jp/~dima/PAPERS/2008ackermann.pdf Cite error: Invalid
<ref>tag; name "k2" defined multiple times with different content Cite error: Invalid<ref>tag; name "k2" defined multiple times with different content - ↑ 5.0 5.1
M.H.Hooshmand. ”Ultra power and ultra exponential functions”. Integral Transforms and
Special Functions 17 (8), 549-558 (2006) Cite error: Invalid
<ref>tag; name "uxp" defined multiple times with different content - ↑ P.Walker. Infinitely differentiable generalized logarithmic and exponential functions. Mathematics of computation, 196 (1991), 723-733.
- ↑ 7.0 7.1 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.
