. Use the Taylor expansion of the function f(z) = 1 1+z [8] 4 centred at...

. Use the Taylor expansion of the function f(z) = 1 1+z [8] 4 centred at the origin z = 0, together with the extended Cauchy Integral Formula to evaluate the contour integrals I C dz/ z^ k (z^ 4 + 1), k = 0, 1, . . . , where C is any positively oriented simple contour going around the origin that is interior to the circle of radius 1 centred at z = 0.

Expert Solution

ANSWER

Cauchy-Goursat Theorem. If a function f is analytic at all points interior to and on a simple closed contour C (i.e., f is analytic on some simply connected domain D containing C), then ∫C f(z) dz = 0. ... However, the Cauchy-Goursat theorem says we don't need to assume that f is continuous (only that it exists!)

Colby Messinger answered 5 months ago

Find the Taylor series or polynomial generated by the following functions a. )f(x) √ x centred...

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