Matlab Code for "The
Apple of My i" can be expressed in only four lines:
psi=inline('1./(1-i*tau).^(n+1)','tau','n');
tau=linspace(-1000,1000,1e6+1)';
n=i;
figure; plot(psi(tau,n)); axis equal
Or, in terms of the
angular variable:
psi=inline('cos(theta).^(n+1).*exp(-i*(n+1)*theta)','theta','n');
theta=linspace(-pi/2,pi/2,1e6+1)';
n=i;
figure; plot(psi(theta,n)); axis equal
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Hahn, Stefan, Hilbert Transforms in Signal Processing,
Artech House, 1996.
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Oliver, Frank, et al, NIST Handbook of Mathematical Functions,
Cambridge, 2010.
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Weisstein, Eric , CRC Encyclopedia of Mathematics,
CRC Press, Chapman and Hall, 2003.
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Zwikker, C., The Advanced Geometry of Plane Curves and
Their Applications, Dover Press, 1963. |
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