Research Article

Some Relations between Stieltjes Transform and Hankel Transform with Applications

Volume: 6 Number: 1 March 31, 2023
Virendra Kumar *
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Communications in Advanced Mathematical Sciences Cover Communications in Advanced Mathematical Sciences
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Some Relations between Stieltjes Transform and Hankel Transform with Applications

Abstract

In the present paper four theorems connecting Stieltjes transform and Hankel transform are established. The theorems are general in nature. Four integral formulae involving special functions are obtained with the help of these theorems. Otherwise it is very difficult to evaluate such type of integrals. Other several integrals may be evaluated with the help of these theorems.

Keywords

Bessel functions, Hankel transform, Stieltjes transform, Struve

Supporting Institution

There is no supporting institution

Project Number

Nil

References

  1. [1] B. R. Bhonsle, A relation between Laplace and Hankel transforms, Proc. Glasgow Math. Assoc., 5(3) (1962), 114-115.
  2. [2] B. R. Bhonsle, A relation between Laplace and Hankel transforms, Math. Japon., 10 (1965), 84-89.
  3. [3] A. Erde ́lyi, W. Magnus, F. Oberhettinger, F. G. Tricomi, Higher Transcendental Functions, vol. II, McGraw-Hill Book Company, New York, 1953.
  4. [4] A. Erde ́lyi, W. Magnus, F. Oberhettinger, F. G. Tricomi, Tables of Integral Transforms, vol. II, McGraw-Hill Book Company, New York, 1954.
  5. [5] K. C. Sharma, Theorems relating Hankel and Meijer’s Bessel transforms, Proc. Glasgow Math. Assoc., 6 (1963), 107–112.
  6. [6] K. C. Gupta, S. M. Agrawal, Unified theorems involving H-function transform and Meijer Bessel function transform, Proc. Indian Acad. Sci. (Math. Sci.), 96 (2) (1987), 125-130.
  7. [7] S. P . Goyal, S. K. Vasishta, Certain relations between generalized Kontorovitch-Lebdev transform and H-function transform, Ranchi Univ. Math. Jour., 6 (1975), 95-102.
  8. [8] S. P. Goyal, R. M. Jain, Certain results for two-dimensional Laplace transform with applications, Proc. Nat. Acad. Sci. India, 59(A) (III) (1989), 407-414.
  9. [9] L. Landau, Monotonicity and bounds for Bessel functions, Proceedings of the Symposium on Mathematical Physics and Quantum Field Theory (Berkeley, California: June 11-13, 1999) (Warchall. H, Editor), Electron J. Differential Equations, Conf. Vol. 04(2000), 147-154.
  10. [10] L. J. Landau, Bessel functions: Monotonicity and bounds, Journal of the London Mathematical Society, 61(1)(2000), 197-215.

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Publication Date

March 31, 2023

Submission Date

December 23, 2022

Acceptance Date

March 29, 2023

Published in Issue

Year 2023 Volume: 6 Number: 1

DOI

https://doi.org/10.33434/cams.1223523

IZ

https://izlik.org/JA87HW96JT

Cite

RIS / Bibtex
APA
Kumar, V. (2023). Some Relations between Stieltjes Transform and Hankel Transform with Applications. Communications in Advanced Mathematical Sciences, 6(1), 60-66. https://doi.org/10.33434/cams.1223523
AMA
1.Kumar V. Some Relations between Stieltjes Transform and Hankel Transform with Applications. Communications in Advanced Mathematical Sciences. 2023;6(1):60-66. doi:10.33434/cams.1223523
Chicago
Kumar, Virendra. 2023. “Some Relations Between Stieltjes Transform and Hankel Transform With Applications”. Communications in Advanced Mathematical Sciences 6 (1): 60-66. https://doi.org/10.33434/cams.1223523.
EndNote
Kumar V (March 1, 2023) Some Relations between Stieltjes Transform and Hankel Transform with Applications. Communications in Advanced Mathematical Sciences 6 1 60–66.
IEEE
[1]V. Kumar, “Some Relations between Stieltjes Transform and Hankel Transform with Applications”, Communications in Advanced Mathematical Sciences, vol. 6, no. 1, pp. 60–66, Mar. 2023, doi: 10.33434/cams.1223523.
ISNAD
Kumar, Virendra. “Some Relations Between Stieltjes Transform and Hankel Transform With Applications”. Communications in Advanced Mathematical Sciences 6/1 (March 1, 2023): 60-66. https://doi.org/10.33434/cams.1223523.
JAMA
1.Kumar V. Some Relations between Stieltjes Transform and Hankel Transform with Applications. Communications in Advanced Mathematical Sciences. 2023;6:60–66.
MLA
Kumar, Virendra. “Some Relations Between Stieltjes Transform and Hankel Transform With Applications”. Communications in Advanced Mathematical Sciences, vol. 6, no. 1, Mar. 2023, pp. 60-66, doi:10.33434/cams.1223523.
Vancouver
1.Virendra Kumar. Some Relations between Stieltjes Transform and Hankel Transform with Applications. Communications in Advanced Mathematical Sciences. 2023 Mar. 1;6(1):60-6. doi:10.33434/cams.1223523

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