Timeline for Solving and Plotting an integral function
Current License: CC BY-SA 4.0
11 events
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| Apr 16, 2019 at 19:25 | comment | added | Ulrich Neumann |
Again the function you are asking for has changed...With the definition I gave in my answer you can solve the sum you called "F[T]": Total[Table[F[m[i]/T],{i,1,n}]
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| Apr 16, 2019 at 15:27 | comment | added | Lele |
I want to sum over something like F[x_?NumericQ] :=NIntegrate[(t Sqrt[t^2-(m[i]/x)^2])/(Exp[t] + 1)/(2*Zeta[3]), {t, m[i]/x, Infinity}] where m[i] is an array of values.. Can I define an array of functions like F[x,i] and then sum over i? It doesn't seem to work indeed...
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| Apr 16, 2019 at 14:23 | comment | added | Lele | Yeah I want to do that, but I would like to know how to manage the list of $m_j$ variables. I am supposing to sum lots of pieces and I would like not to rewrite the function every time, but just using some kind of list of values to sum on, as much as I would do in a for cycle with arrays and stuff like that... | |
| Apr 16, 2019 at 11:12 | comment | added | Ulrich Neumann | Ok, what's the reason not to calculate the single summands numerically as proposed in my answer? | |
| Apr 16, 2019 at 10:45 | comment | added | Lele | Ok sorry, I have to specify that better.. My function is in fact this one: $F(T)=\displaystyle\sum_{j=1}^n\displaystyle\int_{m_j/T}^\infty\dfrac{t\sqrt{t^2-(m_j/T)^2}}{e^t-1}\text{d}t$ | |
| Apr 16, 2019 at 10:31 | comment | added | Ulrich Neumann |
The sum(!) doesn't depend on x and therefor doesn't define F[x]!
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| Apr 16, 2019 at 10:22 | comment | added | Lele | Ok thank you. What if I have to evaluate it in this way: $F(x)=\sum_{j=1}^n\displaystyle\int_{x_j}^\infty\dfrac{t\sqrt{t^2-x_j^2}}{e^t-1}\text{d}t$ where $x_j$ should be a list of values I have to insert somehow... What is the best computational way to do it? | |
| Apr 15, 2019 at 16:16 | comment | added | Bob Hanlon |
@EmanueleCopello - Look at the documentation for PatternTest. Any function which uses numeric techniques such as NIntegrate can only evaluate if its argument(s) is/are numeric, so the argument(s) should be restricted to being numeric.
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| Apr 15, 2019 at 14:21 | comment | added | Lele | Thank you very much, it was silly I guess... Just a brief question: what is the meaning of using "?NumericQ" in the argument of the function? | |
| Apr 15, 2019 at 14:20 | vote | accept | Lele | ||
| Apr 15, 2019 at 14:11 | history | answered | Ulrich Neumann | CC BY-SA 4.0 |