4

There is a lot to unpack here, and probably this is a better question for math.SE. TL; DR version is: in exact arithmetic, this does not converge; see Maxim Umansky's answer. In FP arithmetic, it will converge. I don't know to what, see the long version for an attempt. Let's assume that it is possible to compute $\int_0^{\pi} f_n(x)\text{d}x$ exactly. I don'...


4

There is no finite limit for this series sum. Note that for each $n$ the function $f_n$ is positive definite, $f_n(x) > 0$ within the semi-open interval $(0,\pi]$, and we can construct the lower bound for the sum as follows. Consider some parameter $\epsilon \in (0,\pi]$. Then for each $n$ the integral $\int_0^{\pi} f_n(x) dx \ge \int_0^{\epsilon} f_n(x) ...


2

Curve fitting can be very sensitive to your initial guess for each parameter. Because you don't specify a guess in your code, all of these parameters start with a value of 1. Comparing with the converged results for the t fitting, while t is actually pretty close to 1, the other parameters are much further away. Its mostly just luck that the t value didn't ...


1

NLopt has about a dozen local derivative-free optimizers, including SLSQP in C. Only COBYLA currently supports arbitrary nonlinear inequality and equality constraints; the rest of them support bound-constrained or unconstrained problems only. (However, any of them can be applied to nonlinearly constrained problems by combining them with the augmented ...


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