Timeline for How to use polylogarithm function in c++?
Current License: CC BY-SA 3.0
8 events
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| May 5, 2013 at 19:32 | comment | added | GertVdE | @hardmath: sorry, there was a typo in my upper limit of integration; it should read 5.025 as the OP mentioned, not 5.205 (if you take this, your value is correct). | |
| May 4, 2013 at 20:44 | comment | added | hardmath♦ | @GertVdE: I realize you were making an illustration in support of the larger point (what does OP really want/need), but I get 4.995393138739432 for the specified limits of integration. | |
| May 2, 2013 at 5:55 | comment | added | GertVdE | @flamingohats: it still is not clear whether you need a one shot value ($\int_{0.65}^{5.205} \frac{t^3}{e^t-1}dt = 4.8498308528256668370925$) or if you really need it programmed in your code. If it is the first, why not use Sage, Euler Toolbox, ... to check a number of crucial values for you (either using their polylog implementation or their sophisticated quadrature rules)? If it is the second, implement a "traditional" quadrature method (like you did) and again use Sage, Euler, ... to test and validate it. | |
| May 1, 2013 at 16:36 | comment | added | flamingohats | sorry I got confused. I have approximated the integral from 0.65 to 5.025 using the Trapezoidal method, and I need a formula to find the exact value so that I can compare the approximation with an analytical value. I know this will be approximated because it is a floating point number, so a precision of 1e-6 will be fine. If I can somehow learn how to input the polylog function into the IDE it should work. | |
| Apr 30, 2013 at 15:07 | comment | added | hardmath♦ | @flamingohats: Are you saying you need to approximate $\int_0^x \frac{t^3}{e^t - 1} dt$ for $x \in [0,10]$ or something of that nature? I don't follow why "there will only be two evaluations needed", unless you mean that this is an additional requirement/ideal for the quadrature or other approximation. I'm thinking we can determine a polynomial or rational approximation that gives your required accuracy. | |
| Apr 29, 2013 at 15:08 | comment | added | GertVdE | @flamingohats: then I would go for the expressions in the paper I linked to in my answer. What is your range for $x$? | |
| Apr 29, 2013 at 10:05 | comment | added | flamingohats | Precision needed would be around 10^-6. Do you know any other way which doesn't involve using any extra libraries? | |
| Apr 29, 2013 at 7:38 | history | answered | GertVdE | CC BY-SA 3.0 |