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Functions of a complex variable

Euler's formula, and why complex analysis is where the Riemann Hypothesis lives.

e^{iθ} = cos θ + i sin θ turns rotation into exponentiation, and it is the first step into a subject where differentiable functions are astonishingly rigid: knowing one on a small disc determines it everywhere. The zeta function ζ(s) of the Riemann Hypothesis is such a function; its zeros are the whole story.

Toimiva esimerkki: e^(i*pi)

Arithmetic · Arithmetic

Evaluate -1

-1

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  1. e^{i \pi} = -1

    Power: e^{i \pi} = -1.

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Lisää Analysis

Sequences and their limitsConvergence of seriesImproper integralsTaylor approximation and error