RESULTS ON THE COMMUTATIVE NEUTRIX CONVOLUTION PRODUCT OF DISTRIBUTIONS
Year 2008,
Volume: 37 Issue: 2, 135 - 141, 01.02.2008
B. Jolevska-tuneska
A. Takaci
Abstract
Let Li(x) denote the dilogarithm integral. The goal of this paper is to evaluate several commutative neutrix convolution products involving the dilogarithm integral and its associated functions Li+(x) and Li−(x).
References
- Abramowitz, M. and Stegun, I. A. (Eds) Handbook of Mathematical Functions with formu- las, Graphs and Mathematical Tables, 9th printing(New York: Dover, 1972), 1004-1005.
- van der Corput, J. G. Introduction to the neutrix calculus, J. Analyse Math. 7, 291–398, 1959.
- Fisher, B. and Li, C. K. A commutative neutrix convolution product of distributions, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 23, 13–27, 1993.
- Fisher, B., ¨Oz¸ca˘g, E. and G¨ulen, ¨U. The exponential integral and the commutative neutrix convolution product, J. Analysis 7, 7–20, 1999.
- Jolevska-Tuneska, B., Fisher, B. and ¨Oz¸ca˘g, E. On the dilogarithm integral, submited for publication.
- Gel’fand, I. M. and Shilov, G. E. Generalized functions, Vol. I (Academic Press, 1964), Chap. 1.
- Jones, D. S. The convolution of generalized functions, Quart. J. Math. Oxford 24 (2), 145– 163, 1973.
RESULTS ON THE COMMUTATIVE NEUTRIX CONVOLUTION PRODUCT OF DISTRIBUTIONS
Year 2008,
Volume: 37 Issue: 2, 135 - 141, 01.02.2008
B. Jolevska-tuneska
A. Takaci
References
- Abramowitz, M. and Stegun, I. A. (Eds) Handbook of Mathematical Functions with formu- las, Graphs and Mathematical Tables, 9th printing(New York: Dover, 1972), 1004-1005.
- van der Corput, J. G. Introduction to the neutrix calculus, J. Analyse Math. 7, 291–398, 1959.
- Fisher, B. and Li, C. K. A commutative neutrix convolution product of distributions, Univ. u Novom Sadu Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 23, 13–27, 1993.
- Fisher, B., ¨Oz¸ca˘g, E. and G¨ulen, ¨U. The exponential integral and the commutative neutrix convolution product, J. Analysis 7, 7–20, 1999.
- Jolevska-Tuneska, B., Fisher, B. and ¨Oz¸ca˘g, E. On the dilogarithm integral, submited for publication.
- Gel’fand, I. M. and Shilov, G. E. Generalized functions, Vol. I (Academic Press, 1964), Chap. 1.
- Jones, D. S. The convolution of generalized functions, Quart. J. Math. Oxford 24 (2), 145– 163, 1973.