Numerical Calculations in Clifford Algebra

12Power Series

Power series can be used to implement polynomials and other functions. Within the Clifford numerical suite, pre‐defined power series are provided for calculating trigonometric and hyperbolic functions, logarithmic and exponential functions, reciprocals, and roots. Being implemented as a summation of series, these functions have finite ranges of convergence and have accuracy limited by loss of precision due to imprecise cancellation of alternating terms and by truncation of an infinite number of terms.

12.1 Theory

Power series for a function are implemented in the general form of Eq. (12.1), where the user can specify the values of the coefficients :

(12.1)

The value is the centre of convergence for the expansion. Usually, there are some limits on how far away from the series will converge. Convergence is covered in more detail in Section 12.1.3.

Within the Clifford numerical suite, methods are provided for the user to construct functions by defining their own series, ...