Weyl differintegral
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In mathematics, the Weyl differentintegral is an operator defined, as an example of fractional calculus, on functions f on the unit circle having integral 0 and a Fourier series. In other words there is a Fourier series for f of the form
- Σ aneinθ
with a0 = 0, −∞ < n < ∞.
Then the Weyl differintegral operator of order s is defined on Fourier series by
- Σ (in)saneinθ
where this is defined. Here s can take any real value, and for integer values k of s the series expansion is the expected k-th derivative, if k > 0, or −k-th indefinite integral normalized by integration from θ = 0.
The condition a0 = 0 here plays the obvious role of excluding the need to consider division by zero. The definition is due to Hermann Weyl (1917).
