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Published in:
An Introduction to Quaternions Read chapter Read first chapter

2014 | OriginalPaper | Chapter

5. Exponents and Logarithms

Authors : João Pedro Morais, Svetlin Georgiev, Wolfgang Sprößig

Published in: Real Quaternionic Calculus Handbook

Publisher: Springer Basel

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Abstract

The real exponential and logarithmic functions play an important role in advanced mathematics, including applications to calculus, differential equations, and complex analysis. In this chapter we use the properties of quaternions described in the previous chapters to define and study the quaternionic analogues of these functions.

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previous chapter Quaternion Series and Infinite Products
next chapter Trigonometric Functions
Footnotes
1
It is not trivial to define the quaternion exponential function. Here, we prefer to do this through a power series expansion.
 
2
This constant is defined as the limit \(e =\lim _{n\rightarrow \infty }\bigg{(1 + \frac{1} {n}\bigg)}^{n}\).
 
3
The branch corresponding to n = 0 is known as the principal branch, therefore the values that the function takes along this branch are known as principal values.
 
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Metadata
Title
Exponents and Logarithms
Authors
João Pedro Morais
Svetlin Georgiev
Wolfgang Sprößig
Copyright Year
2014
Publisher
Springer Basel
Book
Real Quaternionic Calculus Handbook

Print ISBN: 978-3-0348-0621-3

Electronic ISBN: 978-3-0348-0622-0

Copyright Year: 2014

DOI
https://doi.org/10.1007/978-3-0348-0622-0_5

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