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 Using a summation in a function		  New Topic  Reply to Topic
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timothy.v.duncan

USA
3 Posts
Posted - 03/04/2010 :  1:00:21 PM  Show Profile  Edit Topic  Reply with Quote  View user's IP address  Delete Topic
Origin Ver. and Service Release (Select Help-->About Origin): 8.1 SR1
Operating System: XP SP3

I would like to fit to a function of the form:

y(x) = C*(x)^(-0.5) * SUM [-(D/x)*(2*n+1)^2]

where C and D are the fitting parameters and the summation is over n from zero to infinity.

I am not really sure how to proceed. I've done simple user-defined functions before but I guess the summation is sort of throwing me off here. Any suggestions would be welcome.

timothy.v.duncan

USA
3 Posts
Posted - 03/04/2010 :  1:03:09 PM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Forgive me, the correct function is

y(x) = C*(x)^(-0.5) * SUM [exp(-(D/x)*(2*n+1)^2)]
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larry_lan

China
Posts
Posted - 03/04/2010 :  8:31:55 PM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Maybe this example can help.

Thanks
Larry
OriginLab Technical Services
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timothy.v.duncan

USA
3 Posts
Posted - 03/05/2010 :  10:28:37 AM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
Thanks for the link. However (and please correct me if I'm wrong), this appears to be a method for integration, when I need a method for an infinite summation.
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larry_lan

China
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Posted - 03/07/2010 :  8:55:29 PM  Show Profile  Edit Reply  Reply with Quote  View user's IP address  Delete Reply
This example already shows how to do semi-infinite integration. You can define similar function like that using a different terminate condition. Or you can also call a NAG function to do infinite integration. Like this example that calls nag_1d_quad_inf_1 function to do one-dimensional adaptive quadrature over infinite or semi-infinite interval.

Thanks
Larry
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