Calculating infinite series of roots

[Stevetuc]

(08-31-2019 12:59 AM)Helge Gabert Wrote:  

(08-30-2019 11:57 PM)ijabbott Wrote:  In fact it only converges for real \(x\) in the interval \(\big[e^{-e}, e^\frac{1}{e}\big]\) (approx. \([0.066, 1.445]\)).

Yes, very true, and that was shown by Euler (back in the days . . . ).

Support for the LambertW function would be nice, if there is ever an update again!

This cas program uses fsolve to calc Lambert fn

Code:


#cas
lmb(z):=
fsolve(equal(w*e^w-z,0),w)
#end

Graph from wikipedia


If z <0 lmb(z) returns both principal and negative branch solutions :

lmb(-0.5/e) returns [−2.67834699002,−0.231960952987]

lmb(-1/e) returns −0.999999842597 (negative and principal branch converge at -1 when z=-1/e)

lmb(1) returns 0.56714329041

lmb(2) returns 0.852605502014