Approximating the Cosine Integral?
Does anyone know of a semiquick way of approximating Ci(x)? I tried to find an asymptotic expansion for it, but had little luck. Truth be told, I'm not even sure exactly what the definition of asymptotic expansion is. I discovered it while learning about ways of approximating harmonic numbers and Stirling's approximation, and only know that it works for large values. Basically, I'd like it to be valid for high numbers, and this is why I'm trying to use this type of series. Can anyone offer any insight? Thanks a bunch!
Edit: By "semiquick" I meant in terms of simple, nice, elementary functions. I don't care if there are a finite number of terms or not, because to me, more terms = more accuracy. 
As u might have guessed,u cannot express Ci(x) through elementary functions.Asymptotic behavior,series expasion and a lot more can be found here and the next pages.
Daniel. 
Yeah, I knew that it couldn't be expressed in a finite number of elementary functions. But what prevents there from being an asymptotic series which approximates it?

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Daniel. 
Maybe I'm being unclear about what I mean. I'm trying to find what its asymptotic series is. Now, I see on the pages you linked to (page 232) something labelled "Asymptotic series," but it doesn't say what they refer to. Should I assume that 1/z (12!/x²+4!/x^4...) is Ci(x)'s asymptotic series?

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Daniel. 
Well, then, if there is no asymptotic expansion, does anyone know a relatively easy way to calculate it? (without using tables?) Any help is greatly appreciated.

Check the same site for its power series.And pay attention to its convergence radius,which means you cannot compute the function using its power series for arbitrary arguments.
Daniel. 
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