@Carl Love

1. Instead of making a series approximation to the Wronskian, how about first testing via plots that your approximation to the HeunG functions is correct.

Which approximations do you mean in particular?Plotting the series approximations of the heung functions?I've done that... they were correct...

2. Oddly enough when calculating the function HeunG(c,q,a,b,g,d,t) as a series expansion with the coefficients from above (with fixed p and then plotting the function) I can go up to 400 with no problem... It's just the combination of the sum within a sum in this wronskianseries somehow which limits the number of terms to 20/30...I dont know why is that...

3. I dont get what you mean...I'm interested in the 2 point connection problem thus the wronskian here gives me the information about the coefficients. i.e. I want to write the solution about t=0 as a linear combination of the solutions about t=1... thus the mixing...

4. the t is evaluated at t=1/2...since the wronskian in my case is independent of t anyway (because the entire solution is a solution of an ode with no first derivative i.e. of schroedinger type)

5. See 1. what approximations do you mean? same as in 1?Didnt do it since the Heung approximations itsself were right... So should then be the derivatives

All in all I have solved the problem for s=1/2 (though only in mathematica yet but the code as above should be right) but unfortunately when decreasing s there is some limiting value around s~0.15 (I think its where the fourth bound state comes in) where either the convergence gets really bad or vanishes at all...

Like functions as the riemann zeta function which is originally only valid for values larger than 1, one can analytically continue those functions into the entire z plane excluding the singularity which arises from the classic series expansion...Given that... how exactly is that problem solved in maple?i.e. When Calculating the wronskian with the implemented heun functions I can go down to say s=0.1 which is smaller then the limit value s~0.15... But the other way by expanding the wronskian into a series doesnt work for these particular values... only for s>~0.15...