Morera’s theorem is the converse of a theorem named for this mathematician. This mathematician showed that the integral of a complex function around a pole is given by 2πi (“two-pi-i”) times the negative first term of the function’s Laurent series around the pole. If the elements of a sequence get arbitrarily close to each other, the sequence is said to be “[this mathematician’s name].” In addition to a namesake (*) residue theorem, this mathematician discovered sufficient conditions for a function to be complex differentiable alongside Bernhard Riemann. The inner product of two vectors is less than or equal to the product of the norms of the vectors according to an inequality named after, for 10 points, what mathematician and Hermann Schwarz? ■END■
ANSWER: Augustin-Louis Cauchy [accept Cauchy integral theorem; accept Cauchy residue theorem; accept Cauchy sequence; accept Cauchy-Riemann equations; accept Cauchy-Schwarz inequality]
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