Abstract
In this paper, we state some q-analogs of the famous Ramanujan Master Theorem. As an application, we compute some values of Jackson’s q-integrals that involve q-special functions.
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References
Berndt, B.: Ramanujan’s Notebooks, Part I. Springer, New York (1985)
Fitouhi, A., Bettaibi, N., Brahim, K.: The Mellin transform in quantum calculus. Constr. Approx. 23(3), 305–323 (2006)
Gasper, G., Rahman, M.: Basic Hypergeometric Series, Encyclopedia of Mathematics and Its Application, vol. 35. Cambridge University Press, Cambridge (1990)
Hardy, G.H.: Ramanujan. Twelve Lectures on Subjects Suggested by His Life and Work, 3rd edn. Chelsea Publishing Company, New York (1978)
Ismail, M.E.H., Stanton, D.: \(q\)-Taylor theorems, polynomial expansions, and interpolation of entire functions. J. Approx. Theory 123, 125–146 (2003)
Kac, V.G., Cheung, P.: Quantum Calculus. Universitext. Springer, New York (2002)
Mera, M.: The \(q\)-Mellin transform of automorphic forms and converse theorems. Acta Arith. 132, 177–196 (2008)
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Fitouhi, A., Brahim, K. & Bettaibi, N. On some q-versions of the Ramanujan Master Theorem. Ramanujan J 50, 433–458 (2019). https://doi.org/10.1007/s11139-019-00141-4
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DOI: https://doi.org/10.1007/s11139-019-00141-4