A Note on Error Functions and Some Related Special Functions
Abstract
In this note, priority is given to presenting essential information on the fundamental error functions, which play particularly different roles in the natural and engineering sciences, as well as some special functions closely related to them. Subsequently, various special relationships among these functions are highlighted, and finally, some selected applications of these relationships — emphasized through several references — are also proposed for interested readers.
Keywords
References
- [1] A. Erdelyi, W. Magnus, F. Oberhettinge, and F. G. Tricomi, Higher Transcendental Functions, I. McGraw-Hill, New York, Toronto, London, 1953.
- [2] E. D. Rainville, Special Functions, Macmillan: New York, NY, USA, 1960.
- [3] N. N. Lebedev, Special Functions and Their Applications, translated by R. A. Silverman, New Jersey, Prentice-Hall Inc, 1965.
- [4] W. Magnus and F. Oberhettinger, Formulas and Theorems for the Special Functions of Mathematical Physics, New York: Springer -Verlag, 1966.
- [5] M. Abramowitz and I. A. Milton, Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, New York, Dover, 1972.
- [6] G. E. Andrews, R. Askey and R. Roy, Special Functions, Encyclopedia of Mathematics and Its Applications, Cambridge University Press, Cambridge, 1999.
- [7] G. A. Korn and T. M. Korn, Mathematical handbook for scientists and engineers: Definitions, theorems and formulas for reference and review, Dover Publications, 2000.
- [8] R. Beals and R. Wong, Special Functions: A Graduate Text, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 2010.
Details
Primary Language
English
Subjects
Modelling and Simulation, Computational Methods in Fluid Flow, Heat and Mass Transfer (Incl. Computational Fluid Dynamics)
Journal Section
Review
Authors
Hüseyin Irmak
*
0000-0003-1897-6725
Türkiye
Publication Date
March 5, 2026
Submission Date
February 4, 2026
Acceptance Date
February 26, 2026
Published in Issue
Year 2026 Volume: 10 Number: Special