Skip to main content
SpringerLink
Log in

Superfunctions and sqrt of factorial

  • Published:
Moscow University Physics Bulletin Aims and scope

Abstract

The holomorphic function h is constructed such that h h z = z!; this function is interpreted as square root of Factorial.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. I. M. Saraeva, Yu. M. Romanovskii, and A. V. Borisov, Vladimir Dmitrievich Krivchenkov, Ser. Great Scientists of Physic Department of Mosc. State Univ. (Fiz. Fakult. Mosc. Gos. Univ., Moscow, 2008), p. 81 [in Russian]; http://www.phys.msu.ru/rus/about/structure/admin/OTDEL-IZDAT/HISTORY/.

    Google Scholar 

  2. V. M. Gordienko and V. K. Novik, On Time and Faculty, on Cathedra and on me. 70-years from Prof. V. P. Kandidov Birthday (Moscow, 2007) [in Russian]; http://ofvp.phys.msu.ru/pdf/Kandidov_70.pdf.

  3. M. Abramovits and I. Stegun, Handbook on Special Functions (National Bureau of Standards, NY, 1964) [in English].

    Google Scholar 

  4. D. Kouznetsov and H. Trappmann, “Mathematics of Computation,” Preprint ILS UEC (2009, in press); http://www.ils.uec.ac.jp/~dima/PAPERS/2009sqrt2.pdf.

  5. http://en.citizendium.org/wiki/Superfunction.

  6. H. Trappmann, Elementary Superfunctions (Tetration Forum, Berlin, 2009); http://math.eretrandre.org/tet-rationforum/showthread.php?tid=275.

    Google Scholar 

  7. H. Kneser, J. Reine Angew. Mathem. 187, 56 (1950).

    Article  MathSciNet  Google Scholar 

  8. H. Trappmann and D. Kouznetsov, “Uniqueness of Holomorphic Abel Functions,” Preprint ILS UEC (2009); http://www.ils.uec.ac.jp/~dima/PAPERS/2009uniabel.pdf.

  9. D. Kouznetsov, Math. Comput. 78, 1647 (2009).

    Article  MathSciNet  ADS  Google Scholar 

  10. G. Belitskii and Yu. Lubish, Studia Mathem. 134, 135 (1999).

    MATH  Google Scholar 

  11. N. H. Abel, Crelle’s J., No. 2, 389 (1827).

  12. http://en.citizendium.org/wiki/Abel_function

  13. Sun Sui Cheng and Li Wenrong, Analytic Solutions of Functional Equations (World Sci., 2008).

  14. E. Schröder, “Uber Iterierte Funktionen III,” Math. Ann. 3, 296 (1870).

    Article  MathSciNet  Google Scholar 

  15. M. Kuczma, B. Choczewski, and R. Ger, Iterative Functional Equations (Cambridge, 1990).

  16. J. Ecalle, Theory of Holomorphic Invariants, Publ. Mathem. No. 67-74 09 (Paris Univ. U.E.R. Mathem., Orsay, 1970); http://portail.mathdoc.fr/PMO/PDF/E_ECALLE_67_74_09.pdf.

    Google Scholar 

  17. J. Milnor, Dynamics in One Complex Variable (Princeton, 2006).

  18. M. Mueller, Old projects; http://www.math.tu-berlin.de/~mueller/projects.html

  19. D. Kouznetsov, “Ackermann Functions of Complex Argument,” Preprint ILS UEC (2008); http://www.ils.uec.ac.jp/~dima/PAPERS/2008ackermann.pdf.

  20. D. Kouznetsov, Vladikavk. Matem. Zh. (2010, in press); http://www.ils.uec.ac.jp/~dima/PAPERS/2009vladie.pdf.

  21. http://en.citizendium.org/wiki/TetrationDerivatives-Real.jpg/code

  22. D. Kouznetsov and H. Trappmann, Preprint ILS UEC (2009); http://www.ils.uec.ac.jp/~dima/PAPERS/2009fractae.pdf.

  23. http://en.citizendium.org/wiki/ArcGamma.jpg/code

  24. A. Robbins, “Solving for the Analytic Piecewice Extension of Tetration and the Super-Logarithm,” Preprint of Virtual Composer (2000); http://misc.virtualcomposer2000.com/TetrationSuperlog_Robbins.pdf.

Download references

Author information

Authors and Affiliations

  1. Institute for Laser Science, University of Electro-Communications 1-5-1 Chofugaoka, Chofushi, Tokyo, 182-8585, Japan

    D. Kouznetsov

  2. Kameruner Str. 9, 13351, Berlin, Germany

    H. Trappmann

Authors
  1. D. Kouznetsov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Trappmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to D. Kouznetsov.

Additional information

Published in Russian in Vestnik Moskovskogo Universiteta. Fizika, 2010, No. 1, pp. 8–14.

The English-language version of the article was prepared by the authors.

About this article

Cite this article

Kouznetsov, D., Trappmann, H. Superfunctions and sqrt of factorial. Moscow Univ. Phys. 65, 6–12 (2010). https://doi.org/10.3103/S0027134910010029

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0027134910010029

Key words

Search

Navigation