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Discrete index transformations with Bessel and Lommel functions

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Abstract

Discrete analogs of the index transforms, involving Bessel and Lommel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.

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References

  1. Brychkov, Yu.A., Marichev, O.I., Savischenko, N.V. 2018. Handbook of Mellin Transforms. In Advances in Applied Mathematics, Boca Raton: CRC Press.

  2. NIST Digital Library of Mathematical Functions, eds. Olver, F. W. J., Olde Daalhuis, A. B., Lozier, D. W., Schneider, B. I., Boisvert, R. F., Clark, C. W., Miller, B. R., and Saunders, B. V. http://dlmf.nist.gov/, Release 1.0.17 of 2017-12-22.

  3. Prudnikov, A.P., Brychkov, Yu.A., Marichev, O.I. 1986. Integrals and Series. Vol. I: Elementary Functions, Vol. II: Special Functions, 1990. Vol. III: More special functions. New York and London: Gordon and Breach.

  4. Yakubovich, S. 1996. Index Transforms. Singapore: World Scientific Publishing Company.

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Acknowledgements

The work was partially supported by CMUP, which is financed by national funds through FCT (Portugal) under the project with reference UIDB/00144/2020.

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Correspondence to Semyon Yakubovich.

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Communicated by Samy Ponnusamy.

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Yakubovich, S. Discrete index transformations with Bessel and Lommel functions. J Anal 29, 1421–1441 (2021). https://doi.org/10.1007/s41478-021-00320-x

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  • DOI: https://doi.org/10.1007/s41478-021-00320-x

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