log-Series and log-Functions as application of multidual analysis

Authors

  • Farid Messelmi University of Djelfa

DOI:

https://doi.org/10.62918/hjma.v2i1.17

Keywords:

Multidual analysis, Multidual factorial, log-series, log-functions

Abstract

The purpose of this paper is to contribute to the development of the new concept of log-series and log-functions as particular continuation of real power series and real functions in multidual algebra. We will focus for the case of elementary log-functions and we propose some applications to special functions.

References

M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Dover, New York, 1964. ISBN 978-0-486-61272-0.

W. K. Clifford, Preliminary Sketch of Bi-Quaternions, Proc. London Math. Soc., 4 (1873), 381--395.

D. Condurache, A Novel Method for Higher-Order Kinematics in Multibody Systems, Conference: The 9th international conference on advanced composite materials engineering COMAT 2022, 17-18 October- 2022 in Bracsov, Romania.

D. Condurache, Analysis of Higher- Order Kinematics on Multibody Systems with Nilpotent Algebra. In: Petriv{c}, T., Ude, A., Vlajpah, L. (eds) Advances in Service and Industrial Robotics. RAAD 2023. Mechanisms and Machine Science, vol 135. Springer, Cham.

D. Condurache, Higher-Order Kinematics of Lower-Pair Chains with Hyper-Multidual Algebra, ASME 2022 International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (IDETC/CIE2022).

D. Condurache, C. Mihail and I. Popa, Hypercomplex Dual Lie Nilpotent Algebras and Higher-Order Kinematics of Rigid Body, Proceedings of SYROM 2022 & ROBOTICS 2022.

D. Condurache, Hyper-Multidual Algebra and Higher-Order Kinematics, Advances in Robot Kinematics 2022.

D. Condurache, Multidual Algebra and Higher-Order Kinematics, EuCoMeS 2020: New Trends in Mechanism and Machine Science, 48--55.

D. Condurache, Multidual and Dual Lie Algebra Representations of Higher-Order Kinematics, 2022 AAS/AIAA Astrodynamics Specialist Conference At: August 7 - 11, 2022 in Charlotte, North Carolina.

D. Condurache, Product of Exponential Formula of Multidual Quaternions and Higher-Order Kinematics, 9th 2023 International Conference on Control, Decision and Information Technologies (CoDIT 2023) At: Roma.

D. Condurache, M. Cojocari and I. Popa, Multidual Quaternions and Higher-Order Kinematics of Lower-Pair Chain, ECCOMAS Thematic Conference on Multibody Dynamics, July 24 - 28, 2023, Lisbon, Portugal.

W. B. V. Kandasamy and F. Smarandache, Dual Numbers, ZIP Publishing Ohio, 2012.

J. E. Kim, The Corresponding Inverse of Functions of Multidual Complex Variables in Clifford Analysis, J. Nonlinear Sci. Appl., 9 (2016), 4520--4528.

F. Messelmi, Analysis of Dual Functions, Annual Review of Chaos Theory, Bifurcations and Dynamical Systems, Vol. 4 (2013), 37--54.

F. Messelmi, Differential Calculus of Multidual Functions, Annual Review of Chaos Theory, Bifurcations and Dynamical Systems, Vol 10 (2021), 1--15.

F. Messelmi, Multidual Numbers and Their Multidual Functions, Electronic Journal of Mathematical Analysis and Applications, Vol. 3(2) (2015), 154--172.

F. Messelmi, Multidual Algebra, International Journal of Mathematics, Game Theory and Algebra, Vol. 26(1) (2017).

F. Messelmi, Ring of Multidual Integers, International Journal of Mathematics, Game Theory and Algebra}, Vol. 28(4) (2020).

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Published

22-03-2024

How to Cite

Messelmi, F. (2024). log-Series and log-Functions as application of multidual analysis. Hilbert Journal of Mathematical Analysis, 2(1), 046–066. https://doi.org/10.62918/hjma.v2i1.17