Subscribe

Subscribe to our Newsletter and get informed about new publication regulary and special discounts for subscribers!

IJARM > IJARM Volume 12 > Asymptotic Behaviors of Wronskians and Finite...
< Back to Volume

Asymptotic Behaviors of Wronskians and Finite Asymptotic Expansionsin the Real Domain - Part II: Mixed Scales and Exceptional Cases

Full Text PDF

Abstract:

In this second Part of our work we study the asymptotic behaviors of Wronskians involving both regularly- and rapidly-varying functions, Wronskians of slowly-varying functions and other special cases. The results are then applied to the theory of asymptotic expansions in the real domain.

Info:

Periodical:
International Journal of Advanced Research in Mathematics (Volume 12)
Pages:
35-68
Citation:
A. Granata, "Asymptotic Behaviors of Wronskians and Finite Asymptotic Expansionsin the Real Domain - Part II: Mixed Scales and Exceptional Cases", International Journal of Advanced Research in Mathematics, Vol. 12, pp. 35-68, 2018
Online since:
September 2018
Authors:
Export:
Distribution:
References:

[1] A. Granata, Asymptotic behaviors of Wronskians and finite asymptotic expansions in the real domain. Part I: scales of regularly- or rapidly-varying functions, International Journal of Advanced Research in Mathematics. 9 (2017) 1-33.

DOI: https://doi.org/10.18052/www.scipress.com/ijarm.9.1

[2] C. Krattenthaler, Advanced determinant calculus, Séminaire Lotharingien Combin. 42 (1999) (The Andrews Festschrift,), Article B42q, 67 pp. math.CO/9902004.

[3] C. Krattenthaler, Advanced determinant calculus: A complement, Linear Algebra and its Applications. 411 (2005) 68-166.

DOI: https://doi.org/10.1016/j.laa.2005.06.042

[4] A. Granata, The theory of higher-order types of asymptotic variation for differentiable functions. Part I: higher-order regular, smooth and rapid variation, Advances in Pure Mathematics. 6 (2016) 776-816.

DOI: https://doi.org/10.4236/apm.2016.612063

[5] N. Bourbaki, Fonctions d'une variable réelle-Théorie élémentaire, Hermann, Paris, (1976).

[6] A. Granata, The theory of higher-order types of asymptotic variation for differentiable functions. Part II: algebraic operations and types of exponential variation, Advances in Pure Mathematics. 6 (2016) 817-867.

DOI: https://doi.org/10.4236/apm.2016.612064

[7] L. Mirsky, An introduction to linear algebra, Oxford University Press, (1972).

[8] T. Muir, A treatise on the theory of determinants, Revised and enlarged by W.H. Metzler, Dover Publications, New York, (1960).

[9] S. Karlin, Total Positivity. Vol. I, Stanford University Press, Stanford, California, (1968).

[10] R.C. Brunet, Pyramidal composition rules for Wronskians upon Wronskians, Journal of Mathematical Physics, 16(5) (1975) 1112-1116.

DOI: https://doi.org/10.1063/1.522640
Show More Hide
Cited By:
This article has no citations.