A new series expansion for slice regular functions

Details A new series expansion for slice regular functions A new series expansion for slice regular functions

2011-10-19

arxiv.org/abs/1110.4227v1

Mathematics

Complex Variables

20 pages, 1 figure

Scientific paper

A promising theory of quaternion-valued functions of one quaternionic variable, now called slice regular functions, has been introduced in 2006. The basic examples of slice regular functions are power series centered at 0 on their balls of convergence. Conversely, if f is a slice regular function then it admits at each point of its domain an expansion into power series, where the powers are taken with respect to an appropriately defined multiplication *. However, the information provided by such an expansion is somewhat limited by a fact: if the center p of the series does not lie on the real axis then the set of convergence needs not be a Euclidean neighborhood of p. We are now able to construct a new type of expansion that is not affected by this phenomenon: an expansion into series of polynomials valid in open subsets of the domain. Along with this construction, we present applications to the computation of the multiplicities of zeros and of partial derivatives.

Affiliated with

Also associated with

No associations

Rating

A new series expansion for slice regular functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A new series expansion for slice regular functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A new series expansion for slice regular functions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-597272