Galoitica: Journal of Mathematical Structures and Applications
Journal DOI
2834-5568ISSN (Online)
Volume 11 , Issue 1 , PP: 12-24, 2024 | Cite this article as | XML | Html | PDF | Full Length Article
Arwa Hajjari 1 *
Doi: https://doi.org/10.54216/GJMSA.0110102
In this paper, we derive the Bessel's equation of complex order (n + i) from the classical well-known Bessel's equation. In addition, we generalize that recurrence relation from Bessel's equation of order (n) to Bessel equation of complex order (n + i). On the other hand, we present an algorithm to solve the novel complex order equation with many illustrated examples that explain the validity of our approach.
Bessel's equation , complex order , differential equation , partial derivation
[1] Artin, E. The gamma function. Courier Dover Publications, (2015).
[2] Bowman, F. Introduction to Bessel functions. Courier Corporation, Springer, (2012).
[3] Dass H. K. Er. Rajnish Verma, "Higher Engineering Mathematics", First Edition, Springer, (2011).
[4] Fedoryuk, M. V. Asymptotic analysis: linear ordinary differential equations. Springer Science & Business Media, (2012).
[5] Korenev B. G. "Bessel Functions and Their Applications"CRC Press, Springer, (2003).
[6] Kreyszig E. "Advanced Engineering Mathematics", Wiley, Springer,
(2013)
[7] Luke, Y. L. Integrals of Bessel functions. Courier Corporation, (2014)
[8] Markel E. G., "Bessel Functions and Equations of Mathematical Physics", Supervisor, Judith Rivas Ulloa, Leioa, 25 June (2015)
[9] Mclachlan N. W. "Bessel Functions for Engineers", 2nd Edition, Oxford University, Press, London, (1955).
[10] Okrasinski W., L. Płociniczak, "A Note on Fractional Bessel Equation and Its Asymptotics", Fract. Calc. Appl. Anal., 16 (2013).
[11] Robin W., "Ladder-operator Factorization and the Bessel Differential Equations", Math. Forum, 9 (2014).
[12] Thukral A. K. "Factorials of Real Negative and Imaginary Numbers-A new Perspetive", Published (2014).
[13] Khosravian-Arab, H., Dehghan, M., and Eslahchi, M.R., Generalized Bessel’s functions: Theory and thier applications. Math Meth Appl. Sci., 1–22, 2017.
