- #1

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Is there a rational function,not series, that approximates e^x

?

for example (x+1)/(x+3)

?

for example (x+1)/(x+3)

- Thread starter Ledsnyder
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- #1

- 26

- 0

Is there a rational function,not series, that approximates e^x

?

for example (x+1)/(x+3)

?

for example (x+1)/(x+3)

- #2

HallsofIvy

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- #3

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something similar to this:

http://math.stackexchange.com/questions/107292/rapid-approximation-of-tanhx

do you also know of any curve fitting software?

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HallsofIvy

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is a

- #5

pasmith

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Truncating the series after a fixed number of terms is not a good method of evaluating [itex]e^x[/itex] numerically for large [itex]|x|[/itex], since one loses precision from calculating the large values of [itex]x^n[/itex] and [itex]n![/itex] and the remainder may be large.

is avery"rapid" approximation to the exponential.

To the OP: Woolfram gives a couple of continued fraction expressions for [itex]e^x[/itex]; truncating these will give you a rational function approximation. But it is better to use a library function for exp if at all possible.

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mathwonk

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1+x.

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lurflurf

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$$

e^{-x}\sim P(x)/Q(x)\\

\text{where}\\

P(x)=\sum_{k=0}^m \frac{(m+n-k)!m!}{(m+n)!k!(m-k)!}x^k

\\

Q(x)=\sum_{k=0}^n \frac{(m+n-k)!n!}{(m+n)!k!(n-k)!}x^k

$$

matches up to the n+m+1 derivative

see

http://mathworld.wolfram.com/PadeApproximant.html

http://en.wikipedia.org/wiki/Padé_table#An_example_.E2.80.93_the_exponential_function

http://wwwhome.math.utwente.nl/~vajtam/publications/temp00-pade.pdf

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