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We give a possible extension of the definition of quaternionic power series, partial derivatives and vector fields in the case of two (and then several) non commutative (quaternionic) variables. In this setting we also investigate the problem of describing zero functions which are not null functions ...

This paper deals with the problem of finding a continuous extension of the hypercomplex (quaternionic or octonionic) logarithm along (quaternionic or octonionic) paths which avoid the origin. The main difficulty depends upon this fact: while a branch of the complex logarithm can be defined in a smal ...

For a slice-regular quaternionic function ▫$f$▫, the classical exponential function ▫${\mathrm exp} f$▫ is not slice-regular in general. An alternative definition of an exponential function, the ▫$\ast$▫-exponential ▫${\mathrm exp}_\ast$▫, was given in the work by Altavilla and de Fabritiis (2019): ...