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Euler Number

By Kardi Teknomo, PhD.

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Definition

 

Approximation as infinite series

 

Approximation as infinite continued fraction

Or, writing it in one line become

 

Very condense form of continued fraction is show that the continued fraction of has regular pattern of where is increasing even numbers.

 

 

 

MS excel function of Euler number is =EXP(1)

 

Now you can download the Spreadsheet companion of this tutorial and try PI() for different accuracy

For example:

Accuracy

Exp as ratio

Error (computed from PI of MS Excel)

0.1

0.001

0.00001

0.0000001

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This tutorial is copyrighted.

Preferable reference for this tutorial is

Teknomo, Kardi. Continued Fraction. http://people.revoledu.com/kardi/tutorial/ContinuedFraction/index.html

 

 

 

 
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