CVPL4

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Write the Taylor expansion of f(z)=z^5+3z+4\, at z=2\,.

In general, the Taylor expansion around z_0\, is f(z) = \sum_{k=0}^\infty \frac{f^{(k)}(z_0)}{k!}(z-z_0)^k\,.

In this case, f'(z)=5z^4+3, f''(z)=20z^3, f'''(z)=60z^2, f^{(4)}(z)=120z, f^{(5)}(z)=120\,.

So

f(z) = 42 + 83(z-2) + 80(z-2)^2 + 40(z-2)^3 + 10(z-2)^4 + (z-2)^5\,


Main Page : Complex Variables : Polynomials

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