Some Parseval-Goldstein Type Theorems For Generalized Integral Transforms

Yıl 2024, Cilt: 12 Sayı: 2, 81 - 92, 14.04.2024

Durmuş Albayrak

https://doi.org/10.36753/mathenot.1362335

Öz

In this work, we establish some Parseval-Goldstein type identities and relations that include various new generalized integral transforms such as $\mathcal{L}_{\alpha,\mu}$-transform and generalized Stieltjes transform. In addition, we evaluated improper integrals of some fundamental and special functions using our results.

Anahtar Kelimeler

Generalized Laplace transform, Generalized Stieltjes transform, Laplace transform, Parseval-Goldstein theorem

Kaynakça

• [1] Debnath, L., Bhatta, D.: Integral Transforms and Their Applications(3rd ed.). Chapman and Hall/CRC. 2014.
• [2] Yürekli, O.: A Parseval-type theorem applied to certain integral transforms. IMA Journal of Applied Mathematics. 42 (3), 241-249 (1989).
• [3] Yürekli, O.: A theorem on the generalized Stieltjes transform, Journal of Mathematical Analysis and Applications. 168(1), 63-71 (1992).
• [4] Albayrak, D., Dernek, N.: Some relations for the generalized e Gn; e Pn integral transforms and Riemann-Liouville, Weyl integral operators. Gazi University Journal of Science. 36 (1), 362-381 (2023).
• [5] Albayrak, D., Dernek, N.: On some generalized integral transforms and Parseval-Goldstein type relations. Hacettepe Journal of Mathematics and Statistics. 50 (2), 526-540 (2021).
• [6] Karataş, H. B., Kumar, D., Uçar, F.: Some iteration and Parseval-Goldstein type identities with their applications. Advances in Mathematical Sciences and Applications. 29 (2), 563–574 (2020).
• [7] Karataş, H. B., Albayrak, D., Uçar, F.: Some Parseval-Goldstein type identities with illustrative examples. Proceedings of the Institute of Mathematics and Mechanics. 49 (1), 60-68 (2023).
• [8] Albayrak, D.: Theory and applications on a new generalized Laplace-type integral transform. Mathematical Methods in the Applied Sciences. 46 (4), 4363-4378 (2023).
• [9] Yürekli, O., Sadek, I.: A Parseval Goldstein type theorem on the Widder potential and its applications. International Journal of Mathematics and Mathematical Sciences. 14, 160375, 517-524 (1991).
• [10] Al-Musallam, F., Kiryakova, V., Tuan, V. K.: A multi-index Borel-Dzrbashjan transform. Rocky Mountain Journal of Mathematics. 32 (2), 409–428 (2002).
• [11] Dzhrbashyan, M. M.: Integral Transforms and Representations of Functions in the Complex Domain. Nauka, Moscow. 1966.
• [12] Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F. G.: Tables of Integral Transforms. Vol. II. New York- Toronto-London. McGraw-Hill Book Company. Inc. 1954.
• [13] Widder, D. V.: A transform related to the Poisson integral for a half-plane. Duke Mathematical Journal. 33 (2), 355–362 (1966).
• [14] Glasser, M. L.: Some Bessel function integrals. Kyungpook Mathematical Journal. 13 (2), 171–174 (1973).
• [15] Dernek, N., Kurt, V., ¸Sim¸sek, Y., Yürekli, O.: A generalization of the Widder potential transform and applications. Integral Transforms and Special Functions. 22 (6), 391-401 (2011).
• [16] Oldham, K. B., Spanier, J., Myland, J.: An Atlas of Functions. Springer. 2010.
• [17] Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F. G.: Tables of Integral Transforms. Vol. I. New York- Toronto-London. McGraw-Hill Book Company. Inc. 1954.
• [18] Ferreira, J., Salinas, S.: A gamma type distribution involving a confluent hypergeometric function of the second kind. Revista Técnica de la Facultad de Ingeniería Universidad del Zulia. 33 (2), 169-175 (2010).