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Some Relations between Stieltjes Transform and Hankel Transform with Applications

Yıl 2023, Cilt: 6 Sayı: 1, 60 - 66, 31.03.2023

Virendra Kumar

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

Öz

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.

Anahtar Kelimeler

Bessel functions Hankel transform Stieltjes transform Struve

Destekleyen Kurum

There is no supporting institution

Proje Numarası

Nil

Kaynakça

  • [1] B. R. Bhonsle, A relation between Laplace and Hankel transforms, Proc. Glasgow Math. Assoc., 5(3) (1962), 114-115.
  • [2] B. R. Bhonsle, A relation between Laplace and Hankel transforms, Math. Japon., 10 (1965), 84-89.
  • [3] A. Erde ́lyi, W. Magnus, F. Oberhettinger, F. G. Tricomi, Higher Transcendental Functions, vol. II, McGraw-Hill Book Company, New York, 1953.
  • [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] K. C. Sharma, Theorems relating Hankel and Meijer’s Bessel transforms, Proc. Glasgow Math. Assoc., 6 (1963), 107–112.
  • [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] 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] 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] 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] L. J. Landau, Bessel functions: Monotonicity and bounds, Journal of the London Mathematical Society, 61(1)(2000), 197-215.
  • [11] A. P. Prudnikov, Yu. A. Brychkov, O. I, Marichev, Integrals and Series: Volume 2. Elementary Functions, Gordon and Breach Science Publishers, New York, 1986.
  • [12] A. P. Prudnikov, Yu. A. Brychkov, O. I, Marichev, Integrals and Series: Volume 2. Special Functions, Gordon and Breach Science Publishers, New York, 1986.
  • [13] I. N. Sneddon, Fourier Transforms, McGraw-Hill, New York, 1951.
  • [14] R. K. Saxena, A relation between generalized Laplace and Hankel transforms, Math. Zeitschr., 81 (1963), 414-415
  • [15] H. M. Srivastava, A relation between Meijer and generalized Hankel transforms, Math. Japon., 11 (1966), 11-13.
  • [16] H. M. Srivastava, On a relation between Laplace and Hankel transforms, Matematiche (Catania), 21 (1966), 199-202.
  • [17] H. M. Srivastava, O. D. Vyas, A theorem relating generalized Hankel and Whittaker transforms, Indagationes Mathematicae (Proceedings), 72(2) (1969), 140-144.
  • [18] H. M. Srivastava, Some remarks on a generalization of the Stieltjes transform, Publ. Math. Debrecen, 23 (1976), 119-122.
  • [19] H. M. Srivastava, V. K. Tuan, A new convolution theorem for the Stieltjes transform & its application to a class of singular integral equations, Arch. Math. (Basel) 64(2) (1995), 144-149.
  • [20] H.M.Srivastava,O.Yu ̈rekli,AtheoremonaStieltjes-typeintegraltransform&itsapplications,ComplexVariables, Theory Appl., 28(2) (1995), 159-168.
  • [21] S. Yakubovich, M. Martins, On the iterated Stieltjes transform & its convolution with application to singular integral equations, Integral Transforms Spec. Funct., 25(5) (2013), doi: 10.1080/10652469.2013.868457

Yıl 2023, Cilt: 6 Sayı: 1, 60 - 66, 31.03.2023

Virendra Kumar

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

Öz

Proje Numarası

Nil

Kaynakça

  • [1] B. R. Bhonsle, A relation between Laplace and Hankel transforms, Proc. Glasgow Math. Assoc., 5(3) (1962), 114-115.
  • [2] B. R. Bhonsle, A relation between Laplace and Hankel transforms, Math. Japon., 10 (1965), 84-89.
  • [3] A. Erde ́lyi, W. Magnus, F. Oberhettinger, F. G. Tricomi, Higher Transcendental Functions, vol. II, McGraw-Hill Book Company, New York, 1953.
  • [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] K. C. Sharma, Theorems relating Hankel and Meijer’s Bessel transforms, Proc. Glasgow Math. Assoc., 6 (1963), 107–112.
  • [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] 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] 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] 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] L. J. Landau, Bessel functions: Monotonicity and bounds, Journal of the London Mathematical Society, 61(1)(2000), 197-215.
  • [11] A. P. Prudnikov, Yu. A. Brychkov, O. I, Marichev, Integrals and Series: Volume 2. Elementary Functions, Gordon and Breach Science Publishers, New York, 1986.
  • [12] A. P. Prudnikov, Yu. A. Brychkov, O. I, Marichev, Integrals and Series: Volume 2. Special Functions, Gordon and Breach Science Publishers, New York, 1986.
  • [13] I. N. Sneddon, Fourier Transforms, McGraw-Hill, New York, 1951.
  • [14] R. K. Saxena, A relation between generalized Laplace and Hankel transforms, Math. Zeitschr., 81 (1963), 414-415
  • [15] H. M. Srivastava, A relation between Meijer and generalized Hankel transforms, Math. Japon., 11 (1966), 11-13.
  • [16] H. M. Srivastava, On a relation between Laplace and Hankel transforms, Matematiche (Catania), 21 (1966), 199-202.
  • [17] H. M. Srivastava, O. D. Vyas, A theorem relating generalized Hankel and Whittaker transforms, Indagationes Mathematicae (Proceedings), 72(2) (1969), 140-144.
  • [18] H. M. Srivastava, Some remarks on a generalization of the Stieltjes transform, Publ. Math. Debrecen, 23 (1976), 119-122.
  • [19] H. M. Srivastava, V. K. Tuan, A new convolution theorem for the Stieltjes transform & its application to a class of singular integral equations, Arch. Math. (Basel) 64(2) (1995), 144-149.
  • [20] H.M.Srivastava,O.Yu ̈rekli,AtheoremonaStieltjes-typeintegraltransform&itsapplications,ComplexVariables, Theory Appl., 28(2) (1995), 159-168.
  • [21] S. Yakubovich, M. Martins, On the iterated Stieltjes transform & its convolution with application to singular integral equations, Integral Transforms Spec. Funct., 25(5) (2013), doi: 10.1080/10652469.2013.868457
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Virendra Kumar 0000-0003-3597-1571

Proje Numarası Nil
Yayımlanma Tarihi 31 Mart 2023
Gönderilme Tarihi 23 Aralık 2022
Kabul Tarihi 29 Mart 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 6 Sayı: 1

Kaynak Göster

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 Kumar V. Some Relations between Stieltjes Transform and Hankel Transform with Applications. Communications in Advanced Mathematical Sciences. Mart 2023;6(1):60-66. doi:10.33434/cams.1223523
Chicago Kumar, Virendra. “Some Relations Between Stieltjes Transform and Hankel Transform With Applications”. Communications in Advanced Mathematical Sciences 6, sy. 1 (Mart 2023): 60-66. https://doi.org/10.33434/cams.1223523.
EndNote Kumar V (01 Mart 2023) Some Relations between Stieltjes Transform and Hankel Transform with Applications. Communications in Advanced Mathematical Sciences 6 1 60–66.
IEEE V. Kumar, “Some Relations between Stieltjes Transform and Hankel Transform with Applications”, Communications in Advanced Mathematical Sciences, c. 6, sy. 1, ss. 60–66, 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 (Mart 2023), 60-66. https://doi.org/10.33434/cams.1223523.
JAMA 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, c. 6, sy. 1, 2023, ss. 60-66, doi:10.33434/cams.1223523.
Vancouver Kumar V. Some Relations between Stieltjes Transform and Hankel Transform with Applications. Communications in Advanced Mathematical Sciences. 2023;6(1):60-6.
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