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Discrete Index Whittaker Transforms

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Abstract

Discrete analogs of the index Whittaker transform are introduced and investigated. It involves series and integrals with respect to a second parameter of the Whittaker function \(W_{\mu , {i n} }(x), \ x >0, \ \mu \in \mathbb {R}, \ n \in \mathbb {N}, \ i \) is the imaginary unit. The corresponding inversion formulas for suitable functions and sequences in terms of these series and integrals are established.

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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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  1. Department of Mathematics, Faculty of Sciences, University of Porto, Campo Alegre st., 687, 4169-007, Porto, Portugal

    Semyon Yakubovich

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  1. Semyon Yakubovich
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Correspondence to Semyon Yakubovich.

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Yakubovich, S. Discrete Index Whittaker Transforms. Results Math 76, 106 (2021). https://doi.org/10.1007/s00025-021-01419-0

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  • DOI: https://doi.org/10.1007/s00025-021-01419-0

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