Some transcendence properties of integrals of Bessel functions
-
2025
Downloads
-
2297
Views
Authors
Gulsah Oner
- Dokuz Eylul University, 35210 Izmir, Turkey.
Mikhail V. Neschadim
- Sobolev Institute of Mathematics and Novosibirsk State University, Novosibirsk, 630090, Russia.
Tahsin Oner
- Department of Mathematics, Ege University, 35100 Izmir, Turkey.
Abstract
We prove that some integrals of Bessel functions are transcendence over ring of Bessel functions with coefficients from the
field of rational fractions of one variable.
Share and Cite
ISRP Style
Gulsah Oner, Mikhail V. Neschadim, Tahsin Oner, Some transcendence properties of integrals of Bessel functions, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 1, 316--324
AMA Style
Oner Gulsah, Neschadim Mikhail V., Oner Tahsin, Some transcendence properties of integrals of Bessel functions. J. Nonlinear Sci. Appl. (2017); 10(1):316--324
Chicago/Turabian Style
Oner, Gulsah, Neschadim, Mikhail V., Oner, Tahsin. "Some transcendence properties of integrals of Bessel functions." Journal of Nonlinear Sciences and Applications, 10, no. 1 (2017): 316--324
Keywords
- Independence
- differential algebra
- Bessel functions
- transcendence properties.
MSC
References
-
[1]
N. I. Fel’dman, A. B. ShidlovskiÄ , The development and present state of the theory of transcendental numbers, (Russian) Uspehi Mat. Nauk, 22 (1967), 3–81.
-
[2]
O. Holder, Memoire sur la fonction \(\Gamma\), Math. Annal, (1887), 1–13.
-
[3]
I. Kaplansky , An introduction to differential algebra, Actualités Sci. Ind., Publ. Inst. Math. Univ. Nancago, Hermann, Paris (1957)
-
[4]
E. R. Kolchin , Extensions of differential fields I, II, III., Ann. Math., 43 (1942), 724–729, Ann. Math., 45 (1944), 358–361, BAMS, 53 (1947), 397–401.
-
[5]
L. Markus, Differential independence of meromorphic functions, University of Minnesota Research Report, (2003), 1–34.
-
[6]
F. W. J. Olver, Asymptotics and special functions, Computer Science and Applied Mathematics. Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York-London (1974)
-
[7]
J. F. Ritt, Integration in Finite Terms, Liouville’s Theory of Elementary Methods, Columbia University Press, , New York, N. Y. (1948)
-
[8]
J. F. Ritt , Differential algebra, American Mathematical Society Colloquium Publications, Vol. XXXIII, American Mathematical Society, New York, N. Y. (1950)
-
[9]
A. B. ShidlovskiÄ, Transcendental numbers, Translated from the Russian by Neal Koblitz, With a foreword by W. Dale Brownawell, De Gruyter Studies in Mathematics, Walter de Gruyter & Co., Berlin (1989)
-
[10]
A. B. ShidlovskiÄ, Transcendence of values of E-functions that are solutions of second-order linear differential equations, (Russian), translated from Mat. Sb, 184 (1993), 75–84 Russian Acad. Sci. Sb. Math., 79 (1994), 63–71.
-
[11]
P. Sibuya, A remark on Bessel functions, Differential equations, dynamical systems, and control science, Lecture Notes in Pure and Appl. Math., Dekker, New York, 152 (1994), 301–306.
-
[12]
C. L Siegel, Über einige Anwendungen diophantischer Approximationen, Abhandlungen der Preussischen Akademie der Wissenschaften, Physicalisch mathematische klasse 1929, Nr 1; (German) [On some applications of Diophantine approximations], 81–138, Quad./Monogr., 2, Ed. Norm., Pisa (2014)
-
[13]
G. N. Watson, A treatise on the theory of Bessel functions, Cambridge University Press, Cambridge, England, The Macmillan Company, New York (1944)