Obtaining a more accurate calculator?

[Michio Cuckoo]

I'm trying to calculate relativistic photon energy shifts, and I have to use e^{\frac{x}{c^{2}}}
However,since I'm dealing with the speed of light, the exponent becomes extremely small and my TI-84 gives me a nonsensical value.

Could anyone recommend a more accurate calculator?

 

[haruspex]

I'm trying to calculate relativistic photon energy shifts, and I have to use e^{\frac{x}{c^{2}}}
However,since I'm dealing with the speed of light, the exponent becomes extremely small

If \frac{x}{c^{2}} is that small, how inaccurate would it be to approximate the answer as 1+\frac{x}{c^{2}}?

 

[Michio Cuckoo]

so you think i should use maclaurin's expansion?

 

[Millennial]

Yes, just cut the first two terms. By the Lagrange form of the remainder, we obtain that an upper bound for the error can be given by \displaystyle \frac{x^{k+1}}{(k+1)!c^{2k+2}} in a Taylor polynomial of degree k. Taking k as two (the above case), we obtain that an upper bound of the error is \displaystyle \frac{x^3}{6c^6}, which, as long as x\leq c, is accurate to at least 5 decimal places.

 

[haruspex]

Yes, just cut the first two terms. By the Lagrange form of the remainder, we obtain that an upper bound for the error can be given by \displaystyle \frac{x^{k+1}}{(k+1)!c^{2k+2}} in a Taylor polynomial of degree k. Taking k as two (the above case), we obtain that an upper bound of the error is \displaystyle \frac{x^3}{6c^6}, which, as long as x\leq c, is accurate to at least 5 decimal places.

That would be taking the first 3 terms, no? Sure, that should be fine, but the first two terms might be enough. How big is x/c², and how accurate do you need the answer to be?

 

[coolul007]

There are some online large number calculators. here's one I found:

http://www.alpertron.com.ar/BIGCALC.HTM

 

[Michio Cuckoo]

That would be taking the first 3 terms, no? Sure, that should be fine, but the first two terms might be enough. How big is x/c², and how accurate do you need the answer to be?

my answer would be in the range of 10^-11 eV.

 

[Michio Cuckoo]

There are some online large number calculators. here's one I found:

http://www.alpertron.com.ar/BIGCALC.HTM

thanks.

 

[haruspex]

my answer would be in the range of 10^-11 eV.

x/c² has units? Doesn't seem right. What exactly does x represent?