Calculating the value of e: Difference between revisions
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2.71828 |
2.71828 |
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</pre> |
</pre> |
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This is a floating point value (and, thus, accurate to 16 decimal places (15 places after the decimal point, in this example)). |
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The unary power verb ^ uses Euler's number as the base, hence |
The unary power verb ^ uses Euler's number as the base, hence |
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</pre> |
</pre> |
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If we need higher accuracy, we can use an approximation expressed as a rational number. To compute e: find the sum as insert plus +/ of the reciprocals % of factorials ! of integers i. . Using x to denote extended precision integers j will give long precision decimal expansions of rational numbers. Format ": several expansions to verify the number of valid digits to the expansion. Let's try for arbitrary digits. |
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<pre> |
<pre> |
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NB. approximation to e as a rational number |
NB. approximation to e as a rational number |
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NB. 31 places shown with 20 terms |
NB. 31 places shown with 20 terms |
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0j30 ": +/ % ! i. x: 20 |
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2.718281828459045234928752728335 |
2.718281828459045234928752728335 |
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NB. 40 terms |
NB. 40 terms |
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0j30 ": +/ % ! i. x: 40 |
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2.718281828459045235360287471353 |
2.718281828459045235360287471353 |
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NB. 50 terms, |
NB. 50 terms, |
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0j30 ": +/ % ! i. x: 50 |
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2.718281828459045235360287471353 |
2.718281828459045235360287471353 |
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