Given a quaternionic slice regular function f, we give a direct and effective way to compute the coefficients of its spherical expansion at any point. Such coefficients are obtained in terms of spherical and slice derivatives of the function itself. Afterwards, we compare the coefficients of f with those of its slice derivative ∂cf obtaining a countable family of differential equations satisfied by any slice regular function. The results are proved in all details and are accompanied to several examples. For some of the results, we also give alternative proofs.
Spherical coefficients of slice regular functions
amedeo altavilla
2021-01-01
Abstract
Given a quaternionic slice regular function f, we give a direct and effective way to compute the coefficients of its spherical expansion at any point. Such coefficients are obtained in terms of spherical and slice derivatives of the function itself. Afterwards, we compare the coefficients of f with those of its slice derivative ∂cf obtaining a countable family of differential equations satisfied by any slice regular function. The results are proved in all details and are accompanied to several examples. For some of the results, we also give alternative proofs.File in questo prodotto:
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