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A grey system means that a system in which part of information is known and part of information is unknown. Formally, grey systems theory describes uncertainty by interval-valued unknowns called grey numbers , with the width of the interval reflecting more or less precise knowledge. [ 3 ]
In mathematics, Cauchy's integral formula, named after Augustin-Louis Cauchy, is a central statement in complex analysis.It expresses the fact that a holomorphic function defined on a disk is completely determined by its values on the boundary of the disk, and it provides integral formulas for all derivatives of a holomorphic function.
In the field of complex analysis in mathematics, the Cauchy–Riemann equations, named after Augustin Cauchy and Bernhard Riemann, consist of a system of two partial differential equations which form a necessary and sufficient condition for a complex function of a complex variable to be complex differentiable.
In complex analysis, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals and infinite series as well.
Formula weight calculator: The input is a chemical molecular formula, using the periodic-table symbols and notation, and there is a button to work out the percentages of its constituents. Astronomical calculator : The input is a date and one or multiple celestial bodies (usually the sun, moon, planets, planetoids or comets).
The simple contour C (black), the zeros of f (blue) and the poles of f (red). Here we have ′ () =. In complex analysis, the argument principle (or Cauchy's argument principle) is a theorem relating the difference between the number of zeros and poles of a meromorphic function to a contour integral of the function's logarithmic derivative.
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As Édouard Goursat showed, Cauchy's integral theorem can be proven assuming only that the complex derivative ′ exists everywhere in . This is significant because one can then prove Cauchy's integral formula for these functions, and from that deduce these functions are infinitely differentiable.