On one sum of Hankel–Clifford integral transforms of Whittaker functions
https://doi.org/10.22405/2226-8383-2019-20-3-349-360
Abstract
In [11], the authors considered the realization T of SO(2, 2)-representation in a space of homogeneous functions on 2×4-matrices. In this sequel, we aim to compute matrix elements of the identical operator T(e) and representation operator T(g) for an appropriate g with respect to the mixed basis related to two different bases in the SO(2, 2)-carrier space and evaluate some improper integrals involving a product of Bessel-Clifford and Whittaker functions. The obtained result can be rewritten in terms of Hankel-Clifford integral transforms and their analogue. The first and the second Hankel-Clifford transforms introduced by Hayek and Pérez–Robayna, respectively, play an important role in the theory of fractional order differential operators (see, e.g., [6, 8]). The similar result have been derived recently by the authors for the regular Coulomb function in [12].
About the Authors
Junesang ChoiKorea, Republic of
Alexander Ivanovich Nizhnikov
Russian Federation
Ilya Anatolevich Shilin
Russian Federation
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Review
For citations:
Choi J., Nizhnikov A.I., Shilin I.A. On one sum of Hankel–Clifford integral transforms of Whittaker functions. Chebyshevskii Sbornik. 2019;20(3):349-360. https://doi.org/10.22405/2226-8383-2019-20-3-349-360
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