Revista de Matemática: Teoría y Aplicaciones ISSN Impreso: 1409-2433 ISSN electrónico: 2215-3373

OAI: https://revistas.ucr.ac.cr/index.php/matematica/oai
Zeroes of generalized Fresnel complementary integral functions
Vol. 23 No. 2 (2016), Articles
Vol. 23 No. 2 (2016)

Zeroes of generalized Fresnel complementary integral functions

Articles
https://doi.org/10.15517/rmta.v23i2.25151
Published August 4, 2016
Jaime Lobo-Segura
CIMPA, Universidad de Costa Rica, San José, Costa Rica
Mario Alberto Villalobos-Arias
CIMPA, Universidad de Costa Rica, San José, Costa Rica
PDF
PS
DVI

Keywords

Fresnel complementary integrals
zeroes of functions
theoretical bounds for zeroes
gamma distribution
complementarias de Fresnel
ceros de funciones
cotas teóricas para ceros
distribución gamma

How to Cite

Lobo-Segura, J., & Villalobos-Arias, M. A. (2016). Zeroes of generalized Fresnel complementary integral functions. Revista De Matemática: Teoría Y Aplicaciones, 23(2), 321–338. https://doi.org/10.15517/rmta.v23i2.25151
ACM ACS APA ABNT Chicago Harvard IEEE MLA Turabian Vancouver

Download Citation

Endnote/Zotero/Mendeley (RIS) BibTeX
Crossref
Scopus
Google Scholar
Europe PMC

Abstract

Theoretical upper and lower bounds are established for zeroes of a parametric family of functions which are defined by integrals of the same type as the Fresnel complementary integral. Asymptotic properties for these bounds are obtained as well as monotony properties of the localization intervals. Given the value of the parameter an analytical-numerical procedure is deduced to enclose all zeros of a given function with an a priori error.

https://doi.org/10.15517/rmta.v23i2.25151
PDF
PS
DVI

References

Abramowitz, M.; Stegun, I.A. (1964) Handbook of Mathematical Functions. National Bureau of Standards, Applied Mathematics Series 55, Washington DC.

Apostol, T. (1975)Mathematical Analysis. Addison Wesley, USA.

Erdélyi, A.; Magnus, W.; Oberhettinger, F.; Tricomi, F.G. (Eds.) (1953) Higher Transcendental Functions, Volume 1. 1. McGraw-Hill, New York.

Koumandos, S.; Lamprecht, M. (2012) “The zeros of certain Lommel functions”, Proceedings of The American Mathematical Society 140(9): 3091–3100.

Kreyszig, E. (1957) “On the complementary functions of the Fresnel integrals”, Canadian Journal of Mathematics 9(4): 500–510.

Lindvall, T. (2002) Lectures on the Coupling Method. Dover, New York.

Livingstone, A.E. (1954) “The zeros of a certain class of indefinite integrals”, Proceedings of the American Mathematical Society 5(2): 296–300.

Livingstone, A.E.; Lorch, L. (1956) “The zeros of certain sine-like integrals”, Proceedings of the American Mathematical Society 7(5): 813–816.

Loya, P. (2005) “Dirichlet and Fresnel integrals via iterated integration”, Mathematics Magazine 78(1): 63–67.

NIST Digital Library of Mathematical Functions (2016) “8.21 Generalized Sine and Cosine Integrals”, http://dlmf.nist.gov/8.21, consulted: Jannuary 25, 2016.

Comments

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Copyright (c) 2016 Revista de Matemática: Teoría y Aplicaciones

Downloads

Download data is not yet available.