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In mathematics, the Weyl integral (named after Hermann Weyl) 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
The theory of fractional integration for periodic functions (therefore including the "boundary condition" of repeating after a period) is given by the Weyl integral. It is defined on Fourier series , and requires the constant Fourier coefficient to vanish (thus, it applies to functions on the unit circle whose integrals evaluate to zero).
In mathematics, the Weyl integration formula, introduced by Hermann Weyl, is an integration formula for a compact connected Lie group G in terms of a maximal torus T. Precisely, it says [ 1 ] there exists a real-valued continuous function u on T such that for every class function f on G :
Category: Fractional calculus. 4 languages. ... Weyl integral This page was last edited on 1 October 2014, at 03:17 (UTC). Text is available under the Creative ...
is the fractional derivative (if q > 0) or fractional integral (if q < 0). If q = 0, then the q-th differintegral of a function is the function itself. In the context of fractional integration and differentiation, there are several definitions of the differintegral.
In mathematics, an Erdélyi–Kober operator is a fractional integration operation introduced by Arthur Erdélyi and Hermann Kober . The Erdélyi–Kober fractional integral is given by x − ν − α + 1 Γ ( α ) ∫ 0 x ( t − x ) α − 1 t − α − ν f ( t ) d t {\displaystyle {\frac {x^{-\nu -\alpha +1}}{\Gamma (\alpha )}}\int _{0 ...
This is not precluded by the weyl differintegral being linked from the fractional calculus discussion, as well as discussed therein. Wikipedia is not heriarchial. Kevin Baas 17:04, 23 Apr 2004 (UTC) If this integral calculus satisfies the rule of Weyl differintegral defined on Wiki, can Wyel differintegral be applied to the integral calculus?
Therefore, after dividing by n and letting n tend to infinity, the left hand side tends to zero, and Weyl's criterion is satisfied. Conversely, notice that if α is rational then this sequence is not equidistributed modulo 1, because there are only a finite number of options for the fractional part of a j = jα.