Euler Number

By Kardi Teknomo, PhD .

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Definition Euler Number

Approximation as infinite series

Euler Number

Approximation as infinite continued fraction

Euler Number

Or, writing it in one line become

Euler Number

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

Euler Number

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

Example:

Accuracy

Exp as ratio

Error (computed from PI of MS Excel)

0.1

Euler Number

Euler Number

0.001

Euler Number

Euler Number

0.00001

Euler Number

Euler Number

0.0000001

Euler Number

Euler Number

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This tutorial is copyrighted .

Preferable reference for this tutorial is

Teknomo, Kardi (2015) Continued Fraction. http://people.revoledu.com/kardi/tutorial/ContinuedFraction/index.html