I have a summation of the form:
$$y(x) = \sum\limits_{h=-L}^L\frac{A(h)\cdot R(h)^2}{((x-h)^2+R(h)^2)^{3/2}}$$
Where I wish to solve/optimise $R(h)$ (leaving $A(h) = const/h$) or $R(h)$ and $A(h)$ such that: $y(x) = mx + c$ for a range of $x$
Is there any way to analytically solve this? Perhaps by using orthogonal functions and decomposing the equation and then summing the coefficients?
For numeric solving the numbers are:
$L = 0.05$
$h$ = 101 values
$A(h)$ would ideally be constant so would be $(const/h)$
The range of validity for $x$ (where $y \approx mx+c$) would ideally be between 0.01 and 0.04
What would be the best way to code this for a numeric solution?
Thanks in advance for any help!