We present a constructive description of monogenic functions that take values in a three-dimensional commutative harmonic algebra with one-dimensional radical by using analytic functions of complex variable. It is shown that monogenic functions have the Gâteaux derivatives of all orders.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 5, pp. 670–680, May, 2013.
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Plaksa, S.A., Pukhtaevich, R.P. Constructive description of monogenic functions in a three-dimensional harmonic algebra with one-dimensional radical. Ukr Math J 65, 740–751 (2013). https://doi.org/10.1007/s11253-013-0810-x
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DOI: https://doi.org/10.1007/s11253-013-0810-x