The Yukawa Potential Function and Reciprocal Univalent Function


  • Amir Pishkoo Physics department-Nuclear Science Research School (NSTRI)
  • Maslina Darus 2School of Mathematical Sciences, Faculty of Science and Technology Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor Darul.Ehsan, Malaysia



Strong and weak nuclear force, Univalent functions, Meromorphic univalent functions, reciprocal theorem, Meijer's G-function.


This paper presents a mathematical model that provides analytic connection between four fundamental forces (interactions), by using modified reciprocal theorem,derived in the paper, as a convenient template. The essential premise of this work is to demonstrate that if we obtain with a form of the Yukawa potential function [as a meromorphic univalent function], we may eventually obtain the Coloumb Potential as a univalent function outside of the unit disk. Finally, we introduce the new problem statement about assigning Meijer's G-functions to Yukawa and Coloumb potentials as an open problem.


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Duren, P.-L. 1983 Univalent Functions. New York: Springer-Verlag.

Mao, Zhiqiang, and Huifang Liu, Meromorphic Functions in the Unit Disc That Share Values in an Angular Domain, Journal of Mathematical Analysis and Applications, 359 (2009), 444-450.

Ganczar, Andrzej, An Extremal Problem for Harmonic Self-mappings of the Unit Disk, Journal of Mathematical Analysis and Applications, 329 (2007), 46-50.

Korhonen, Risto, and Jouni Rättyä, Finite Order Solutions of Linear Differential Equations in the Unit Disc, Journal of Mathematical Analysis and Applications, 349 (2009), 43-54.

Goodman, A.-W. 1983 Univalent Functions. USA: University Of South Florida.

Abe, Sumiyoshi, Invariants for Time-dependent Fermion Systems, Physics Letters A, 181 (1993), 359-365.

Yamazaki, T. and Yoshinori , A Pseudo Invariant Masses of Hadrons in Nuclei, Nuclear Physics A, 654 (1999), 552c - 555c.

Martin, B. R. 2009 Nuclear and Particle Physics: An Introduction. Wiley.

Kiryakova, V. 1994 Generalized Fractional Calculus and Applications. UK: Longman- Harlow.

Askey, R. A. 2010 Meijer G-function., In Adri, D, Olde, B (eds.) NIST Handbook of Mathematical Functions. Cambridge University Press, Cambridge.

A. Pishkoo, M. Darus, Fractional differintegral transformation of univalent Meijer’s G-functions. Journal of Inequalities and Applications 2012 (2012) article 36.


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How to Cite

Pishkoo, A., & Darus, M. (2013). The Yukawa Potential Function and Reciprocal Univalent Function. JOURNAL OF ADVANCES IN PHYSICS, 3(2), 197–202.