Is there a MATLAB implementation of Dickman's rho function?

Good morning,

does anyone know if there's an implementation of Dickman's rho function (see Wikipedia) in MATLAB? (In fact, I'm primarily interested in the function , for fixed y.)

If there isn't, would it help if I filed a feature request to have this implemented by MathWorks for a future MATLAB release?

Thanks & have a nice weekend!

Answer 1

[NN]

Hi,

As per my knowledge, there is not implementation of Dickman’s rho function in MATLAB.

Since the function is satisfies the differential equation, you can implement the function using ‘dsolve’ MATLAB function.

Documentation: https://in.mathworks.com/help/symbolic/solve-a-single-differential-equation.html

But you can always file a feature request to have this implemented for a future MATLAB release.

Hope this helps.

Regards,

Narvik

[Christian Schröder]

Hi Narvik,

thanks for the suggestion. I'm not sure that this is a viable avenue given that there appears to be no general closed-form solution for Dickman's rho, but I'm certainly willing to give it a try! However, the following did not work:

syms rho(u)

eq = u*diff(rho,u) + rho(u-1)==0

cond = rho(u)==1

rhoSol = dsolve(eq, cond)

Instead, this first produces a warning ("Number of equations greater than number of indeterminates. Trying heuristics to reduce to square system."), and then an error ("Unable to reduce to square system because the number of equations differs from the number of indeterminates.")

I have zero experience with dsolve however, so if you have any tips on how to make this work I'm all ears.

Thanks again & all the best!