Abstract
The aim of this paper is to obtain Parseval–Goldstein type relations for the index \({ }_2 F_1\)-transform.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data Availability
The manuscript has no associated data.
References
Erdélyi, A., Magnus, W., Oberhettinger, F., Tricomi, F.: Higher Transcendental Functions, vol. I. McGraw-Hill Book Company Inc, New York-Toronto-London (1953)
Prudnikov, A.P., Brychkov, Y.A., Marichev, O.I.: Integrals and Series, vol. 3. Gordon and Breach Science Publishers, New York (1990)
González, B.J., Negrín, E.R.: \(L^p\)-Inequalities and Parseval-type relations for the index \(_2F_1\)-transform. Filomat 37(4), 1087–1095 (2023)
Olver, F.W.J.: Asymptotics and Special Functions. Academic Press, New York (1974)
Wimp, J.: A class of integral transforms. Proc. Edinburgh Math. Soc. 14(2), 33–40 (1964)
Choi, J., Kachhia, K.B., Prajapati, J.C., Purohit, S.D.: Some integral transforms involving extended generalized Gauss hypergeometric functions. Commun. Korean Math. Soc. 31(4), 779–790 (2016)
Hayek, N., González, B.J., Negrín, E.R.: Abelian theorems for the index \(_2F_1\)-transform. Rev. Técn. Fac. Ingr. Univ. Zulia 15(3), 167–171 (1992)
Hayek, N., González, B.J.: Abelian theorems for the generalized index \(_2 F_1\)-transform. Rev. Acad. Canaria Cienc. 4(1–2), 23–29 (1992)
Hayek, N., González, B.J.: A convolution theorem for the index \(_2F_1\)-transform. J. Inst. Math. Comput. Sci. Math. Ser. 6(1), 21–24 (1993)
Hayek, N., González, B.J.: The index \(_2F_1\)-transform of generalized functions. Comment. Math. Univ. Carolin. 34(4), 657–671 (1993)
Hayek, N., González, B.J.: On the distributional index \(_2F_1\)-transform. Math. Nachr. 165, 15–24 (1994)
Hayek, N., González, B.J.: An operational calculus for the index \(_2F_1\)-transform. Jñānābha 24, 13–18 (1994)
Hayek, N., González, B.J.: A convolution theorem for the distributional index \(_2F_1\)-transform. Rev. Roumaine Math. Pures Appl. 42(7–8), 567–578 (1997)
Goldstein, S.: Operational Representations of Whittaker’s Confluent Hypergeometric Function and Weber’s Parabolic Cylinder Function. Proc. Lond. Math. Soc. 2(34), 103–125 (1932)
Yürekli, O.: A Parseval-type theorem applied to certain integral transforms. IMA J. Appl. Math. 42, 241–249 (1989)
Acknowledgements
The authors are very thankful to the reviewer for his/her valuable and constructive comments and suggestions.
Funding
The authors have not disclosed any funding.
Author information
Authors and Affiliations
Contributions
All authors contributed equally.
Corresponding author
Ethics declarations
Conflict of interest
No potential conflict of interest was reported by the authors.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Maan, J., Negrín, E.R. Parseval–Goldstein Type Theorems for the Index \({ }_2 F_1\)-Transform. Int. J. Appl. Comput. Math 10, 69 (2024). https://doi.org/10.1007/s40819-024-01713-9
Accepted:
Published:
DOI: https://doi.org/10.1007/s40819-024-01713-9