Editing Trigonometric interpolation (section)

==Formulation in the complex plane==
The problem becomes more natural if we formulate it in the [[complex plane]]. We can rewrite the formula for a trigonometric polynomial as
<math> p(x) = \sum_{k=-K}^K c_k e^{ikx}, \, </math>
where ''i'' is the [[imaginary unit]]. If we set ''z'' = ''e''<sup>''ix''</sup>, then this becomes
:<math> q(z) = \sum_{k=-K}^K c_k z^{k}, \, </math>
with
:<math> q(e^{ix}) \triangleq p(x). \, </math>
This reduces the problem of trigonometric interpolation to that of polynomial interpolation on the [[unit circle]]. Existence and uniqueness for trigonometric interpolation now follows immediately from the corresponding results for polynomial interpolation.

For more information on formulation of trigonometric interpolating polynomials in the complex plane, see p.&nbsp;156 of [http://www.physics.arizona.edu/~restrepo/475A/Notes/sourcea.pdf Interpolation using Fourier Polynomials].