## 5428 Reputation

17 years, 271 days
Munich, Germany

## fsolve ?...

@acer

Yes, I am using Windows. I "played" with it using some other solver and it works. Thus it may be a problem with fsolve for this task. And for example plotting is ok.

## ok...

@fkohlhepp ok, now one should proceed with acer's approach, "alternative", https://www.mapleprimes.com/questions/234625-How-Do-You-Implement-Recursion#comment288258

which is based on Rouben's translation to Maple https://www.mapleprimes.com/questions/234625-How-Do-You-Implement-Recursion#answer288250

## @acer Neat :-) However fsolve(IIf, ...

Neat :-) However fsolve(IIf, 7..8) and U(6) unfortunately does not work for me using Maple 2021.2, the calls return unevaluated.

U(8.3) works

## Hm ......

f:= r -> eqn2(6*Unit('degree'), r*Unit('m'/'sec'))/Unit(N);

# plot(f, 5 .. 10, numpoints=3); # ok

fsolve(f, 7 .. 8);
7.74974018709663

## as pdf ?...

@fkohlhepp I do not know Maple Flow - but you may try to print / export as pdf

For that you may also try to replace lower case int(...) by Upper Case Int(...)

Edit: try to write
Thust := (theta, u) -> N__bld*Int(th__s(r, theta, u), r = R__hng .. R__tip);

Edit 2: moreover you may feed (your original) Thust with some test values to check whether you will get numerical values (otherwise fsolve can not work).

## Well (3)...

Yes, just eqn2(theta) should be enough (and we do not have or need your csv data).

Or complete the attached Maple sheet, MP_234625_1.mw

And it is likely the problem adressed by acer

## Well (2)...

You could print your final eqn(2) or your function (I mean print = ready for copy paste, not just a picture) and post it, no?

## Well...

Well, it is on you

## Why ......

Why do you not upload a Maple Worksheet, just containing the mathematical equation and constants (without unit)?

## Step 2: Vbar(s) = ......

Vbar(s) =

9/3200*(2^(4/5)*exp(4*s)+(-4/3*s-1)*2^(4/5))*exp(-4*s)*(exp(2)*2^(1/10)-1/10*(-\
1)^(9/10)*GAMMA(1/10,-2)+1/10/sin(1/10*Pi)*(-1)^(9/10)/GAMMA(9/10)*Pi)+9/3200*(
100/33*GAMMA(9/10)*2^(9/10)*WhittakerM(-1/20,11/20,4*s)*s^(1/20)*exp(2*s)*sin(1
/10*Pi)-800/11*GAMMA(9/10)*s^(11/10)*exp(4*s)*sin(1/10*Pi)+(320/3*exp(4*s)-320/
9)*Pi)*exp(-4*s)/Pi

Find the sheet attached, including some numerical cross check by plotting

MP_234576.mw

## Example 5...

For Example 5 there is an easy but ugly workaround: decompose it

 > #
 > restart; interface(version);

Example 5 . Regular singular point. Complex roots

 > Order:=6;   ode:=x^3*diff(y(x),x\$2)+sin(x^3)*diff(y(x),x)+x*y(x)=0; sol:=dsolve(ode,y(x),type='series',x=0): # simplify(%); sol1:=eval(%, _C2=0): sol2:=eval(%%, _C1=0):
 (1.1)
 > 'rhs(sol1)+rhs(sol2)= rhs(sol)'; is(%);
 (1.2)
 > rhs(sol1): Y:= unapply(%, x): eval(lhs(ode), y=Y): MultiSeries:-asympt(%, x): convert(%,polynom);
 (1)
 > rhs(sol2): Y:= unapply(%, x): eval(lhs(ode), y=Y): MultiSeries:-asympt(%, x): convert(%,polynom);
 (2)
 >

## ok, it is just a bit dense...

@ecterrab Thank you, it is just that the FunctionAdvisor is a bit short (for me) in its condition for the definition, but reading again it becomes clear what is meant by e1,e2,e3

## 3.60773264994268*10^29...

Done more carefully it is 3.60773264994268*10^29

MP_234318_(2).mw

## many terms...

Have you estimated how many terms are involved?

Edit: moreover in one case you use LegendreP as summation index - that will not work. Try starting with "1" oder "2" instead of "9"

## a short way...

Here is a short way to get it in trigonometrics, like dharr, but using the parameters

 > # https://www.mapleprimes.com/questions/234277-How-To-Solve-A-Cubic-Assuming-Discriminant
 > restart;
 > f := 2*y^3*z - y^2 -2*m; assume(m<0, 0
 (1)
 > S:=[solve(f,y)]:
 > map(evalc@Im, S); # to show that all solutions are real
 (2)
 > map(evalc@Re, S): simplify(%, {discrim(f,y)=discr}): # more easy to read Z:=simplify(%), discr = 'discrim(f,y)'; #%;
 (3)
 >