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Algorithms to approximate numerically a root of a nonlinear equation or system: for instance, Newton's method, secant method, bisection, etc.

1 vote
1 answer
422 views

When does this limiting ratio give a real root $x$ to the equation of the form $\sum\limits_...

By searching the Inverse Symbolic Calculator, we appear to be able to make the following conjecture about a real root to the equation: $$\sum\limits_{k=0}^d \frac{x^k a_{k+1}}{k!}=0 \tag{1}$$ Let the …
1 vote
0 answers
202 views

Is it possible in principle (but not in practice) to recursively factor away the Riemann zet...

Let: $$f_0(x)=\frac{\zeta (x)}{\sin \left(\frac{\pi x}{2}\right)}$$ and let the seed point be: $$s=\sqrt{-1}$$ which is the input into the limit: $$\rho_1=s+\lim\limits_{n \rightarrow \infty}\left(1- …