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Student Support Forum: 'von Mangoldt Lambda series acting "funny"' topicStudent Support Forum > General > "von Mangoldt Lambda series acting "funny""

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10/05/09 5:10pm

Im working with both Dirichlet and power series involving von Mangoldt Lambda function, and Im often times getting the following error:
[code]MangoldtLambda::exact: Argument 18.` in MangoldtLambda[18.] is not an exact number. >>
General::stop: Further output of MangoldtLambda::exact will be suppressed during this calculation. >>[/code]
A simple example giving this error is [code]NSum[MangoldtLambda[n]/(n^2),{n,1,Infinity}][/code]
(which is actually the log derivative of the Riemann Zeta evaluated at s=2).
According to the error message the problem is that for some reason Mathematica stops feeding MandoldtLambda[n] into the computation after the first 18-19 members, which seems to be confirmed by the fact that this same sum from above "converges" for like s=0, and that of course is total nonsense. So, my question is: What am I doing wrong or is that some flaw in Mathematica or bit of both? :) It would be also nice to know how to avoid these errors resp. how to make Mathematica yield correct numerical values for series involving von Mangoldt Lambda function.

Thanks in advance for any advice!


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