Download page: https://www.maplesoft.com/download/

Then enter your purchse code (= the one after "The following Purchase Codes activate this product")

@Carl Love Thank you, my fault (guess I believed the search function)

MmaTranslator:-FromMma("Hypergeometric0F1Regularized[a, z]");
> diff(%, a):
> subs(z=1, %): limit(%, a=1); evalf(%);

                        hypergeom([], [a], z)
                        ---------------------
                              GAMMA(a)

                         D[1](BesselI)(0, 2)

                          -0.113893872749533

@ThomasLev 

You have to plot over r = abs(L - R) .. L + R (not around 0), which is r = 37917000000000.0 .. 38683000000000.0

PS and a (serious) advice: do not use lower case letter l in coding to avoid misreading between 1,l and I

Why the answer given by MMA is complete?

I have no more idea that actually works

Edit: especially since the system seems to have non-isolated zeros, i.e. the zero locus has positive dimension

"wanted" and "the following form" and using numbers only is a bit vague ...

Since you have one solution already: from where is it taken?

Edit: the following solves your system as well

u[1] = 1.39974334087917*10^20,
u[2] = -8.58840568689494*10^19,
v[1] = -4.06871292861560*10^18,
v[2] = 5.40018729250301*10^19,
v[5] = -1.88749250437202*10^19
u[4]=-u[1], u[3]=-u[2], u[5]=0,
v[4]=v[1], v[3]=v[2]

Looking for the asymptotics of 1/sinh(x) and trying a brute guess, Maple recognizes that 1/sinh(x) < 2*2/exp(x). Feeding exp(x)/4 instead of sinh(x) it can be seen that the modified series converges and Maple finds its symbolic sum (roughly twice).

I guess the poster means

w :=  - 1/2 * sqrt(Pol(k, 8))

because he uses dw/dk and asks where w is real (thus not a constant)

Could it be that Mathcad operates elementwise on vectors? Maple does not ...

@Kitonum that is even more simple, yes

You can not use the VectorCalculus package?

@one man why not also posting your worksheet for that?

This is what I get opening Cengel2.mw using Maple 2021.2 (which asks for repairing it and warns me about auto execution) and save it as Cengel2_1.mw

Cengel2_1.mw

Download MP_235397.mw