Summary

Generated from the following Python script:

   import numpy as np
   import numpy.polynomial.chebyshev as np_cheby
   import matplotlib.pyplot as pl
   def f(x): 
       x = np.asarray(x)
       with np.errstate(divide='ignore'):
           return 1 / (x - 3)
   ftilde = np_cheby.Chebyshev.interpolate(f, 5)
   tk, _ = np_cheby.chebgauss(5)
   pl.figure(figsize=(5,4))
   x = np.linspace(-2, 4, 121)
   xint = np.linspace(-1, 1, 101)
   pl.plot(x, f(x), '-r', label='$(y-3)^{-1}$')
   pl.plot([3,3], [-10,10], ':r', lw=1)
   pl.plot(xint, ftilde(xint), '-k', label=r'$P_5(y)$')
   pl.plot(x, ftilde(x), '--k', lw=1.2)
   pl.plot(tk, ftilde(tk), '+k', lw=1, label='Chebyshev nodes')
   pl.legend()
   pl.ylim(-5, 5)
   pl.xlim(-1.5, 4)
   pl.title(r"Local expansion of a pole at $x=3$")

Licensing

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