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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.
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).
Just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis, the double integral of a positive function of two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where z = f(x, y)) and the plane which contains its domain. [1]
Lists of integrals; Integral transform; Leibniz integral rule; Definitions; Antiderivative; Integral Riemann integral; Lebesgue integration; Contour integration; Integral of inverse functions; Integration by; Parts; Discs; Cylindrical shells; Substitution (trigonometric, tangent half-angle, Euler) Euler's formula; Partial fractions (Heaviside's ...
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 following is a list of integrals (antiderivative functions) of rational functions. Any rational function can be integrated by partial fraction decomposition of the function into a sum of functions of the form:
Download as PDF; Printable version; From Wikipedia, the free encyclopedia. Redirect page. Redirect to: Fractional calculus#Fractional integrals; Retrieved from "https
Download as PDF; Printable version; In other projects ... Pages in category "Fractional calculus" ... Weyl integral This page was last ...
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