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Evaluation of Holomorphic Ackermanns

Received: 21 November 2014     Accepted: 17 December 2014     Published: 27 December 2014
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Abstract

Holomorphic extension of the Ackermann function is suggested. Algorithms of evaluation of tetration and pentation are discussed and illustrated with explicit plots and complex maps.

Published in Applied and Computational Mathematics (Volume 3, Issue 6)
DOI 10.11648/j.acm.20140306.14
Page(s) 307-314
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2014. Published by Science Publishing Group

Keywords

Ackermann Function, Superfunction, Tetration, Pentationx

References
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[2] http://link.springer.com/article/10.1007%2FBF01459088 Wilhelm Ackermann. Zum Hilbertschen Aufbau der reellen Zahlen. Mathematische Annalen 99, Number 1(1928), Z.118-133.
[3] http://www.tandfonline.com/doi/abs/10.1080/10652460500422247#.VI7FoBaD5N2 M.H.Hooshmand, August 2006, ”Ultra power and ultra exponential functions”, Integral Transforms and Special Functions, Vol. 17, No. 8, 549-558.
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[6] http://mizugadro.mydns.jp/PAPERS/2009vladie.pdf http://www.ils.uec.ac.jp/~dima/PAPERS/2009vladie.pdf D.Kouznetsov. Tetration as special function. Vladikavkazskii Matematicheskii Zhurnal, 2010, v.12. issue 2, p.31-45.
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[8] http://www.ams.org/journals/mcom/2010-79-271/S0025-5718-10-02342-2/home.html https://www.researchgate.net/publication/220576905_Portrait_of_the_four_regular_super-exponentials_to_base_sqrt%282%29 http://eretrandre.org/rb/files/Kouznetsov2009_215.pdf http://www.ils.uec.ac.jp/~dima/PAPERS/2010q2.pdf http://mizugadro.mydns.jp/PAPERS/2010q2.pdf D.Kouznetsov, H.Trappmann. Portrait of the four regular superexponentials to base sqrt(2). Mathematics of Computation, 2010, v.79, p.1727-1756.
[9] http://link.springer.com/article/10.3103%2FS0027134910010029 https://www.researchgate.net/publication/226675861_Superfunctions_and_sqrt_of_factorial D.Kouznetsov, H.Trappmann. Superfunctions and square root of factorial. Moscow University Physics Bulletin, 2010, v.65, No.1, p.6-12. (Russian version: p.8-14)
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  • APA Style

    Dmitrii Kouznetsov. (2014). Evaluation of Holomorphic Ackermanns. Applied and Computational Mathematics, 3(6), 307-314. https://doi.org/10.11648/j.acm.20140306.14

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    ACS Style

    Dmitrii Kouznetsov. Evaluation of Holomorphic Ackermanns. Appl. Comput. Math. 2014, 3(6), 307-314. doi: 10.11648/j.acm.20140306.14

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    AMA Style

    Dmitrii Kouznetsov. Evaluation of Holomorphic Ackermanns. Appl Comput Math. 2014;3(6):307-314. doi: 10.11648/j.acm.20140306.14

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  • @article{10.11648/j.acm.20140306.14,
      author = {Dmitrii Kouznetsov},
      title = {Evaluation of Holomorphic Ackermanns},
      journal = {Applied and Computational Mathematics},
      volume = {3},
      number = {6},
      pages = {307-314},
      doi = {10.11648/j.acm.20140306.14},
      url = {https://doi.org/10.11648/j.acm.20140306.14},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140306.14},
      abstract = {Holomorphic extension of the Ackermann function is suggested. Algorithms of evaluation of tetration and pentation are discussed and illustrated with explicit plots and complex maps.},
     year = {2014}
    }
    

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    T1  - Evaluation of Holomorphic Ackermanns
    AU  - Dmitrii Kouznetsov
    Y1  - 2014/12/27
    PY  - 2014
    N1  - https://doi.org/10.11648/j.acm.20140306.14
    DO  - 10.11648/j.acm.20140306.14
    T2  - Applied and Computational Mathematics
    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
    SP  - 307
    EP  - 314
    PB  - Science Publishing Group
    SN  - 2328-5613
    UR  - https://doi.org/10.11648/j.acm.20140306.14
    AB  - Holomorphic extension of the Ackermann function is suggested. Algorithms of evaluation of tetration and pentation are discussed and illustrated with explicit plots and complex maps.
    VL  - 3
    IS  - 6
    ER  - 

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

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