Analytical Properties of Power Series on Levi-Civita Fields 1 ...

K. Shamseddine and M. Berz
[9] T. Levi-Civita. Sui numeri transfiniti. Rend. Acc. Lincei, 5a, 7:91,113,
1898.
[10] L. Neder. Modell einer Leibnizschen Differentialrechnung mit aktual
unendlich kleinen Größen. Mathematische Annalen, 118:718–732, 1941-
1943.
[11] W. F. Osgood. Functions <strong>of</strong> Real Variables. G. E. Stechert & CO., New
York, 1938.
[12] S. Priess-Crampe. Angeordnete Strukturen: Gruppen, Körper, projektive
Ebenen. Springer, Berlin, 1983.
[13] P. Ribenboim. Fields: Algebraically Closed and Others. Manuscripta
Mathematica, 75:115–150, 1992.
[14] W. H. Schikh<strong>of</strong>. Ultrametric Calculus: An Introduction to p-Adic Analysis.
Cambridge University Press, 1985.
[15] K. Shamseddine. New Elements <strong>of</strong> Analysis on the Levi-Civita Field.
PhD thesis, Michigan State University, East Lansing, Michigan, USA,
1999. Also Michigan State University report MSUCL-1147.
[16] K. Shamseddine and M. Berz. Exception handling in derivative computation
with non-Archimedean calculus. In M. Berz, C. Bisch<strong>of</strong>,
G. Corliss, and A. Griewank, editors, Computational Differentiation:
Techniques, Applications, and Tools, pages 37–51, Philadelphia, 1996.
SIAM.
[17] K. Shamseddine and M. Berz. Intermediate values and inverse functions
on non-Archimedean fields. International Journal <strong>of</strong> Mathematics and
Mathematical Sciences, 30:165–176, 2002.
[18] K. Shamseddine and M. Berz. Measure theory and integration on the
Levi-Civita field. Contemporary Mathematics, 319:369–387, 2003.
[19] K. Shamseddine and M. Berz. Convergence on the Levi-Civita field and
study <strong>of</strong> power series. In Lecture Notes in Pure and Applied Mathematics,
pages 283–299. Marcel Dekker, Proceedings <strong>of</strong> the Sixth International
Conference on P-adic Analysis, July 2-9, 2000, ISBN 0-8247-
0611-0.
20