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On Some Fourier Analogues of Dual Integrals Involving Bessel Functions and Trigonometrical Kernels
Omprakash Atale1
Section:Research Paper, Product Type: Journal-Paper
Vol.9 ,
Issue.1 , pp.40-42, Feb-2022
Online published on Feb 28, 2022
Copyright © Omprakash Atale . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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IEEE Style Citation: Omprakash Atale, “On Some Fourier Analogues of Dual Integrals Involving Bessel Functions and Trigonometrical Kernels,” International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol.9, Issue.1, pp.40-42, 2022.
MLA Style Citation: Omprakash Atale "On Some Fourier Analogues of Dual Integrals Involving Bessel Functions and Trigonometrical Kernels." International Journal of Scientific Research in Mathematical and Statistical Sciences 9.1 (2022): 40-42.
APA Style Citation: Omprakash Atale, (2022). On Some Fourier Analogues of Dual Integrals Involving Bessel Functions and Trigonometrical Kernels. International Journal of Scientific Research in Mathematical and Statistical Sciences, 9(1), 40-42.
BibTex Style Citation:
@article{Atale_2022,
author = {Omprakash Atale},
title = {On Some Fourier Analogues of Dual Integrals Involving Bessel Functions and Trigonometrical Kernels},
journal = {International Journal of Scientific Research in Mathematical and Statistical Sciences},
issue_date = {2 2022},
volume = {9},
Issue = {1},
month = {2},
year = {2022},
issn = {2347-2693},
pages = {40-42},
url = {https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=2720},
publisher = {IJCSE, Indore, INDIA},
}
RIS Style Citation:
TY - JOUR
UR - https://www.isroset.org/journal/IJSRMSS/full_paper_view.php?paper_id=2720
TI - On Some Fourier Analogues of Dual Integrals Involving Bessel Functions and Trigonometrical Kernels
T2 - International Journal of Scientific Research in Mathematical and Statistical Sciences
AU - Omprakash Atale
PY - 2022
DA - 2022/02/28
PB - IJCSE, Indore, INDIA
SP - 40-42
IS - 1
VL - 9
SN - 2347-2693
ER -
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Abstract :
The aim of our present work is to establish some Fourier type integrals that involve Bessel function and trigonometrical kernels using the Fourier inversion formula that was communicated by S. Ramanujan in his Quarterly Reports. Some possible applications to dual integral equations along with concluding remarks and further directions are presented.
Key-Words / Index Term :
Ramanujan’s Fourier inversion theorem, Dual integrals
References :
[1] I. Sneddon. “Dual integral equations with trigonometrical kernels”. Proceedings of the Glasgow Mathematical Association, Vol. 5, Issue 3, pp. 147-152. 1962.
[2] K. Srivastava. “Dual Integral Equations with Bessel Function and Trigonometrical Kernels”. Proceedings of the Edinburgh Mathematical Society, Vol. 13, Issue 4, pp. 351-354, 1963.
[3] W. Magnus and F. Oberhettinger, “Special functions of mathematical physics”, New York, p. 8, 1949.
[4] B. Berndt, “Ramanujan’s Notebooks Part I”, Springer-Verlag, New York, 1985
[5] G. N. Watson, “The theory of Bessel functions”, Cambridge, 1944.
[6] J. Owndes. “Dual Integral Equations with Trigonometric Kernels. Proceedings of the Edinburgh Mathematical Society,Vol. 15, Issue 1, pp. 73-74, 1966.
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