Sidebar on Mathematica

GUIDE: Mathematics of the Discrete Fourier Transform (DFT) - Julius O. Smith III. Sidebar on Mathematica

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NOTE: THIS DOCUMENT IS OBSOLETE, PLEASE CHECK THE NEW VERSION: "Mathematics of the Discrete Fourier Transform (DFT), with Audio Applications --- Second Edition", by Julius O. Smith III, W3K Publishing, 2007, ISBN 978-0-9745607-4-8. - Copyright © 2017-09-28 by Julius O. Smith III - Center for Computer Research in Music and Acoustics (CCRMA), Stanford University

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Sidebar on Mathematica

Mathematica is a handy tool for cranking out any number of digits intranscendental numbers such as $e$:

In[]:
  N[E,50]
Out[]:
  2.7182818284590452353602874713526624977572470937
Alternatively, we can compute $(1+\ for small $\:
In[]:
  (1+delta)^(1/delta) /. delta->0.001
Out[]:
  2.716923932235594
In[]:
  (1+delta)^(1/delta) /. delta->0.0001
Out[]:
  2.718145926824926
In[]:
  (1+delta)^(1/delta) /. delta->0.00001
Out[]:
  2.718268237192297
What happens if we just go for it and set delta to zero?
In[]:
  (1+delta)^(1/delta) /. delta->0
                                 1
Power::infy: Infinite expression - encountered.
                                 0
Infinity::indt:
                             ComplexInfinity
   Indeterminate expression 1                encountered.
Indeterminate

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