## dharr

Dr. David Harrington

## 5973 Reputation

19 years, 300 days
University of Victoria
Professor or university staff

## Social Networks and Content at Maplesoft.com

I am a professor of chemistry at the University of Victoria, BC, Canada, where my research areas are electrochemistry and surface science. I have been a user of Maple since about 1990.

## MaplePrimes Activity

### These are replies submitted by dharr

I don't know much about this, but in Maple 2015 FunctionAdvisor("branch_cuts",HeunC); returns "The location of the "branch cuts" for HeunC is unknown to the FunctionAdvisor"; compare FunctionAdvisor("branch_cuts",BesselJ); which returns "[BesselJ(a, z), And(a::(Not(integer)), z < 0)]". Likewise, MathematicalFunctions:-Get("branch_cuts",HeunC); returns empty.

There is further information in other parts of the MathematicalFunctions package such as Evalf that may be useful.

## general statement...

@vicky2811 This is a general statement. Polynomials of degree greater than 5 do not have formulas for their roots (except in special cases). See e.g. https://en.wikipedia.org/wiki/Polynomial#Solving_equations

If you are interested in the infinite summation case (c=infinity) then it might be possible to find some formulas.

## improved for indexed variables...

@mmead Glad you liked it. I modified it to also handle indexed variables, where the unit is the same for any index. See the edit in my original answer.

## nice...

@tomleslie I should have noticed that! Vote up.

## Question...

Please specify exactly what you want to do, and what the question is.

## worksheet and question...

Please upload the worksheet by using the green up-arrow, and let us know what the question is.

## eval and subs...

@jrive You used eval(subs(s = I*omega, xfer_in_s)). Simpler is to evaluate at s = I*omega: eval(xfer_in_s, s = I*omega).
eval does automatic simplification where subs does not, and is usually what you want.

@tomleslie I just used that because the OP said "abs (x1(j)-x1(j-1)) < 10^-4 ". I also didn't understand the iteration requirement in relationship to the code given.

## derivatives...

@awass Yes looks like you have to use the original PDE and work out the derivatives numerically from the function. See here for a post about that.

## initial conditions...

The error message is because you now have a system of two pdes, so need two initial conditions. Since u is your time variable, and your only initial condition is f(0,x)=g; you also need h(0,x)=something. The other conditions are boundary conditions. I don't use the numeric pde solver enough to know how to solve your problem.

## varepsilon...

@ I think the constant one is varepsilon, so not the same.

## not solved...

@okokoabraham No I didn't solve it. Hope someone else can help you. [Edit: see below]

## no guarantee...

@matmxhu For transendental equations it will always be hard, which I guess is why allsolutions only says "more solutions". The tryhard option doesn't help here either.

Edit: I guess for these types of second order odes, Sturm-Liouville theory tells you the number of nodes go up by one for each successive eigenfunction, so if you only find half the solutions, you can tell some are missing.

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