[R] sum to infinity
hello,
can i calculate a sum to infinity in R.
i want to do something like this:
\sum_{i=0}^\infty
\frac{2^{-d-1}}{\Gamma(\frac{d-1}{2})}\left(\frac{\Gamma(2d-3)(2-d)_{i}\Gamma(i+1,-z/2)2^{i+1}}{\Gamma(d-1)(4-2d)_{i}i!}\right)+
\\
\sum_{i=0}^\infty
\frac{2^{-d-1}}{\Gamma(\frac{d-1}{2})}\left(\frac{\Gamma(3-2d)(d-1)_{i}\Gamma(2d-2+i,-z/2)2^{2d-2+i}}{\Gamma(2-d)(2d-2)_{i}}\right),
where (a)_{i}=\Gamma(a+i) / \Gamma(a) .
I hope someone can help me.
Tuggi
--
View this message in context:
http://r.789695.n4.nabble.com/sum-to-infinity-tp2537122p2537122.html
Sent from the R help mailing list archive at Nabble.com.
__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
Re: [R] sum to infinity
On Sep 13, 2010, at 5:24 AM, tuggi wrote:
hello,
can i calculate a sum to infinity in R.
i want to do something like this:
\sum_{i=0}^\infty
\frac{2^{-d-1}}{\Gamma(\frac{d-1}{2})}\left(\frac{\Gamma(2d-3)(2-
d)_{i}\Gamma(i+1,-z/2)2^{i+1}}{\Gamma(d-1)(4-2d)_{i}i!}\right)+
\\
\sum_{i=0}^\infty
\frac{2^{-d-1}}{\Gamma(\frac{d-1}{2})}\left(\frac{\Gamma(3-2d)
(d-1)_{i}\Gamma(2d-2+i,-z/2)2^{2d-2+i}}{\Gamma(2-d)(2d-2)_{i}}\right),
where (a)_{i}=\Gamma(a+i) / \Gamma(a) .
I hope someone can help me.
Are you aware of the RYacas interface to the symbolic algebra YACAS.
(I'm not sure I have all the caps set correctly, but your search
engine probably won't care.)
--
David Winsemius, MD
West Hartford, CT
__
R-help@r-project.org mailing list
https://stat.ethz.ch/mailman/listinfo/r-help
PLEASE do read the posting guide http://www.R-project.org/posting-guide.html
and provide commented, minimal, self-contained, reproducible code.
[R] sum to infinity
Hi r-users, How do we evaluate the summation of (1/m!) from 0 to infinity (for example). Any help is very much appreciated. Thank you. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] sum to infinity
Well, sum of 1/m! is e--does that answer your question? Generally, I guess you have to decide how much error you're comfortable with; then using an error approximation formula, you can back out the M at which you can stop the sum. Then you can write a for loop that ends at M. Hope that helps. On Wed, Mar 25, 2009 at 8:43 PM, Roslina Zakaria zrosl...@yahoo.com wrote: Hi r-users, How do we evaluate the summation of (1/m!) from 0 to infinity (for example). Any help is very much appreciated. Thank you. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. [[alternative HTML version deleted]] __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Re: [R] sum to infinity
Dear Roslina, For $m \rightarrow \infty$ that sum is exp(1)-1: options(digits=20) exp(1)-1 [1] 1.718281828459045 m-20 sum(1/factorial(1:20)) [1] 1.718281828459045 HTH, Jorge On Wed, Mar 25, 2009 at 8:43 PM, Roslina Zakaria zrosl...@yahoo.com wrote: Hi r-users, How do we evaluate the summation of (1/m!) from 0 to infinity (for example). Any help is very much appreciated. Thank you. __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. [[alternative HTML version deleted]] __ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
