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Cover: 9786202672863 | Superfunctions | Dmitrii Kouznetsov | Taschenbuch | Paperback | 2020
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Superfunctions
Non-integer iterates of holomorphic functions. Tetration and other superfunctions. Formulas,algorithms,tables,graphics
Taschenbuch von Dmitrii Kouznetsov
Sprache: Englisch

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Beschreibung
Tools for evaluation of superfunctions, abelfunctions and non-integer iterates of holomorphic functions are collected. For a given transferfunction T, the superfunction is solution F of the transfer equation F(z+1)=T(F(z)) . The abelfunction is inverse of F. In particular, superfunctions of factorial, exp, sin are suggested. The Holomorphic extensions of the logistic sequence and those of the Ackermann functions are considered. Among ackermanns, the tetration (mainly to the base b>1) and natural pentation (to base b=e) are presented. The efficient algorithm for the evaluation of superfunctions and abelfunctions are described. The graphics and complex maps are plotted. The possible applications are discussed. Superfunctions significantly extend the set of functions, that can be used in scientific research and technical design. Generators of figures are loaded to [...] for the free downloading. With these generators, the Readers can reproduce (and modify) the figures from the Book. The Book is intended to be applied and popular. I try to avoid the complicated formulas, but some knowledge of the complex arithmetics and the Cauchy integral should help.
Tools for evaluation of superfunctions, abelfunctions and non-integer iterates of holomorphic functions are collected. For a given transferfunction T, the superfunction is solution F of the transfer equation F(z+1)=T(F(z)) . The abelfunction is inverse of F. In particular, superfunctions of factorial, exp, sin are suggested. The Holomorphic extensions of the logistic sequence and those of the Ackermann functions are considered. Among ackermanns, the tetration (mainly to the base b>1) and natural pentation (to base b=e) are presented. The efficient algorithm for the evaluation of superfunctions and abelfunctions are described. The graphics and complex maps are plotted. The possible applications are discussed. Superfunctions significantly extend the set of functions, that can be used in scientific research and technical design. Generators of figures are loaded to [...] for the free downloading. With these generators, the Readers can reproduce (and modify) the figures from the Book. The Book is intended to be applied and popular. I try to avoid the complicated formulas, but some knowledge of the complex arithmetics and the Cauchy integral should help.
Über den Autor
Graduated: Physics Department of the Moscow State University, 1980. Work: USSR, Mexico, USA, Japan. Proven the quantum stability of the optical soliton. Low bound of the quantum noise of nonlinear amplifier. Limit of single mode approximation in Quantum Optics. Theorem on modes of Dirichlet Laplacian. Theory of ridged atomic mirrors. TORI Axioms.
Details
Erscheinungsjahr: 2020
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
ISBN-13: 9786202672863
ISBN-10: 6202672862
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Kouznetsov, Dmitrii
Hersteller: LAP LAMBERT Academic Publishing
Maße: 220 x 150 x 20 mm
Von/Mit: Dmitrii Kouznetsov
Erscheinungsdatum: 28.07.2020
Gewicht: 0,506 kg
Artikel-ID: 119458104
Über den Autor
Graduated: Physics Department of the Moscow State University, 1980. Work: USSR, Mexico, USA, Japan. Proven the quantum stability of the optical soliton. Low bound of the quantum noise of nonlinear amplifier. Limit of single mode approximation in Quantum Optics. Theorem on modes of Dirichlet Laplacian. Theory of ridged atomic mirrors. TORI Axioms.
Details
Erscheinungsjahr: 2020
Fachbereich: Allgemeines
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
ISBN-13: 9786202672863
ISBN-10: 6202672862
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Kouznetsov, Dmitrii
Hersteller: LAP LAMBERT Academic Publishing
Maße: 220 x 150 x 20 mm
Von/Mit: Dmitrii Kouznetsov
Erscheinungsdatum: 28.07.2020
Gewicht: 0,506 kg
Artikel-ID: 119458104
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