Results on the Exponential Integral

Authors

  • T. Zenku
  • B. Jolevska-Tuneska

DOI:

https://doi.org/10.5644/SJM.13.1.05

Keywords:

Exponential integral, exponential function, distribution, convolution

Abstract

Results on the convolution product of the exponential integral and exponential function are given. These results are found in a space of distributions. The convolution products gained in this work may be considered as a generalization of Chandrasekhar's functions which are needed in the problem of diffuse reflections and transmission of radiation by an atmosphere.

Downloads

Download data is not yet available.

References

L. Schwartz, Théorie des distributions, vols. I and II, Actualités Scientifiques et Industrielles, Hermann and Cie, Paris, 1959.

I. N. Sneddon, Special functions of Mathematical Physics and Chemistry, Oliver and Boyd, 1961.

I. M. Gel'fand and G. E. Shilov, Generalized Functions, Vol. I, Academic Press Chap. 1, 1964.

D. S. Jones, The convolution of generalized functions, Quart. J. Math. Oxford, 24 (2)(1973), 145--163.

D. G. Madland and J. R. Nix, New calculation of prompt fission neutron spectra and average prompt neutron multiplicities, Nucl. Sci. Eng., 81 (1982), 213--271.

C. Chiccoli, S. Lorenzutta and G. Maino, Concerning some integral of the generalized exponential-integral function, Computer Math. Appl., 23 (11) (1992), 13--21.

D. H. Werner, J. A. Huffman, A. J. Ferraro and J. K. Breakall, An exact solution of the generalized exponential integral and its application to moment method formulations, Antennas and Propagation, IEEE Transactions on, Volume 41, Issue 12, 1993, DOI: 10.1109/8.273316.

A. H. Zemanian, Distribution theory and transform analysis, Dover Publications, INC, (1995), 122--142.

H. G. Embacher, G. Gurbl and M. Oberguggenberger, Product of distributions in several variables and applications to zero-mass QED2, Z. Anal. Anw., 11 (4) (1996), 437-454.

F. Farassat, Introduction to generalized function with applications in aerodynamics and aeroacoustics, NASA Technical Paper, 3428 (1996), 1-45.

B. Fisher and J. D. Nicholas, The exponential integral and the convolution, SUT. J. Math., 33 (2) (1997), 139--148.

B. Fisher and J. D. Nicholas, The neutrix convolution product of $ei(lambda x)$ and $x^r$, Math. Montisnigri, 9 (1998), 51--64.

B. Fisher, E. Ozcag and U. Gulen, The exponential integral and the commutative neutrix convolution product, J. Analysis, 7 (1999), 7--20.

B. Fisher and J. D. Nicholas, On the exponential integral, Hacet. Bull. Nat. Sci. Eng., 28 (1999), 55--64.

B. Fisher and J. D. Nicholas, The exponential integral and the neutrix convolution product, J. Nat. Sci. Math., 40 (1,2) (2000), 23--36.

B. Fisher and J. D. Nicholas, On the exponential integral and the non-commutative neutrix convolution product, Int. Trans. Spec. Func., 11 (4) (2001), 353--362.

L. Lazarova and B. Jolevska-Tuneska, On the generalized fresnel sine integrals and convolution, Adv. Math. Sci. J., 1 (1) (2012), 65--71.

M. Miteva and B. Jolevska-Tuneska, Some results on the Colombeau product of distributions, Adv. Math. Sci. J., 1 (2) (2012), 121--126.

D. Nemzer, Mikusinski operational calculus approach to the distributional Stieltjes transform, Adv. Math. Sci. J., 2 (1) (2013), 35--42.

B. Fisher and F. Al-Sirehy, Convolutions involving the exponential function and the exponential integral, Math. Morav., accepted for publication.

Downloads

Published

19.05.2017

How to Cite

Zenku, T. ., & Jolevska-Tuneska, B. . (2017). Results on the Exponential Integral. Sarajevo Journal of Mathematics, 13(1), 71–80. https://doi.org/10.5644/SJM.13.1.05

Issue

Section

Articles