Geodesic
Invariants on a set of reciprocal iterated exponential power coefficients
Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 4, pp. 383-391 
A. P. Bulanov. Invariants on a set of reciprocal iterated exponential power coefficients. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, Tome 15 (2015) no. 4, pp. 383-391. http://geodesic.mathdoc.fr/item/ISU_2015_15_4_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

A chain exponent $L_B(z)=z\cdot B(z)$, having a power sequence $\{b_n\}_{n=1}^{\infty}$, $b_n\ne0$, $n=1,2,\ldots$, $\overline{\lim\limits_{n\to\infty}}|b_n|<\infty$, is defined by a function sequence $B(z)=e^{b_1\cdot z\cdot B_1(z)}$, $B_1(z)=e^{b_2\cdot z\cdot B_2(z)}, \ldots, B_{k-1}(z)=e^{b_k\cdot z\cdot B_k(z)},\ldots$ (we use the denotation $B(z)=\langle e^z;b_1,b_2,\ldots\rangle$ in the paper). Similarly, a chain exponent $L_a(w)=w\cdot A(w)$ is defined where $A(w)=\langle e^w;a_1,a_2,\ldots\rangle$, having a power sequence of mutually inverse chain exponents up to the $4$-th order. In the paper, we find the concrete invariant of the $4$-t order expressed by the form of $3$-rd order with respect to powers. We give an example of two number sequences which are the powers of mutually inverse chain exponents adducing the truth of transformations performed.

[1] Bulanov A. P., “About recurrence formula defining indicators of an inverse function of Lambert”, Modern Problems of Function Theory and Their Application, Proc. 16th Saratov Winters School (Saratov, 2012), 29–32 (in Russian)

[2] Dubinov A. E., Galidakis I. N., “Explicit Solution of the Kepler Equation”, Physics of Particles and Nuclei Letters, 4:3 (2007), 213–216 | DOI | MR | Zbl

[3] Galidakis I. N., “On an application of Lambert's $W$ function to infinite exponentials”, Complex Var. Theory Appl., 49:11 (2004), 759–780 | MR | Zbl

[4] Galidacis I. N., “On Solving the $p$-th Complex Auxiliary Equation $f^{(p)}(z)=z$”, Complex Variables, 50:13 (2005), 977–997 | DOI | MR

[5] Bulanov A. P., “Regularity of infinite exponentials”, Izv. Math., 62:5 (1998), 901–928 | DOI | DOI | MR | Zbl

[6] Bulanov A. P., “Infinite iterated power with alternating coefficients”, Sb. Math., 192:11 (2001), 1589–1620 | DOI | DOI | MR | Zbl

[7] Bulanov A. P., “Chain exponents and function Lambert”, Proc. Math. Center named N. I. Lobachevskian, 43, 2011, 64–71 (in Russian)

[8] Bulanov A. P., “On invariants on the set of indicators of mutually inverse functions Lambert submitted chain exhibitors”, Modern Methods of Function Theory and Related Problems, Proc. Voronezh Winters School (Voronezh, 2013), 295–303 (in Russian)

[9] Bulanov A. P., “The sixth indicator is the inverse function of Lambert presented chain exponent”, Complex analysis and applications, VI Petrozavodsk Intern. Conf. (Petrozavodsk, 2012), 5–10 (in Russian)