Heun functions arise in the solutions of various differential equations, for instance for the Schroedinger equation for the hydrogen atom in physics, which is also of chemical interest.  Although they have been nominally included in Maple for several years, they are still in a primitive state; despite their obscurity and intractable nature, there seems not to exist much possibility, within Maple, to convert these functions into better known and characterised functions.  A similar condition holds for Lame and spheroidal functions that are invaluable in the solution of differential equations in physics but are not even mentioned in Maple. 

The compilation of mathematical functions by Abramowitz and Stegun was published half a century ago, but there are still important functions explained therein that are lacking from Maple, not to mention the successor in the NIST Digital Library of Mathematical Functions.

Integral equations are another weak component of Maple; the present content relies on a basis of work of ProfessorCorless and his student submitted to the 'Maple Share Library' -- decades ago.  Forty years ago, David Stoutemyer generated some procedures to solve non-linear integral equations in Reduce, but forty years later Maple has no benefit from that knowledge.

We can only hope that Maple 19 will remedy some of these gross deficiencies.  The teaching, learning and practice of physics will benefit from their implementation.

At the internet site of The Heun Project, a strong declaration is made that only Maple incorporates Heun functions, which arise in the solution of differential equations that are extremely important in physics, such as the solution of Schroedinger's equation for the hydrogen atom.  Indeed solutions appear in Heun functions, which are highly obscure and complicated to use because of their five or six arguments, but when one tries to convert them to another function, nothing seems to work.  For instance, if one inquires of FunctionAdvisor(display, HeunG), the resulting list contains

"The location of the "branch cuts" for HeunG are [sic, is] unknown ..." followed by several other "unknown" and an "unable". Such a solution of a differential equation is hollow.

Incidentally, Maple's treatment of integral equations is very weak -- only linear equations with simple solutions, although procedures by David Stoutemyer from 40 years ago are available to enhance this capability.

When can we expect these aspects of Maple to work properly, for applications in physics?

hi, is there a way to collect all commands in one place which have been used during a clickable math session of a document? in fact this would help in creating automated tasks.

I paste below a simple code illustrating what I want to create: two lists from a set with pairs. I wonder it is a very simple task but I my lists aren't create in the end. 

> restart;
>
> lista:=[[1,10],[2,20],[3,30]]:
> x:=[]:
> y:=[]:
>
> for i from 1 to nops(lista) do
>     for j from 1 to 2 do
>
>         if j = 1 then
>             x[i,j]:=op(1,op(i,lista));
>        fi;
>        if j = 2 then
>             y[i,j]:=op(2,op(i,lista));
>       fi;
>    od;
> od;
>
> x;
> y;

In resume then after the for loop is terminated I want to be left with two lists:

x:= [1,2,3] and y:=[10,20,30]. I'm sure it has a quick fix but I'm stuck and would appreciate any help/advice.  

Thanks in advance!

Dear Maple users

I have a question which is maybe easily solved, but I cannot seem to find the solution myself. A vector X of coefficients has been computed earlier in the Maple document and I want these coefficients placed in front of some written symbols in order to make Maple display the final result in a nice way. I made an attempt with the Vector command as shown in the image, but I cannot make the indices start at -2. In addition I want some written math placed in front of the expression. In fact I want it displayed like shown on the image marked with a red rectangle. I did write this manually, but want Maple to do it automatically when given the coefficients vector calculated earlier. I hope someone can help me here!

(It is about finite difference methods, by the way)

Regards,

Erik 

How to numerically solve the problem

with Maple? Such type problems arise in elasticity theory (for example, see https://zbmath.org/?q=an:01366371).

Edit. Typo in the code:sin(y(x)) instead of sin(x).

How I can get a list of all label refernces of a worksheet. In fact I want to write a small code which would produce the LaTex output (written to a text file) for my indicated labels. thanx

I've got the following double integral over a region A:

e^(1/x*y)/(y^2)*(x+1)^2 where A={(x,y):1/2<=x*y<=2,1<=x<=3}

to evaluate this:

I've tried :

int6:=int(int(e^(1/x*y)/((y^2)*(x+1)^2),x=1..3),y=(1/2)..(2/3));

since the largest lower bound and smallest upper bound for y based on 1/2<=xy<=2 are 1/2 and 2/3 respectively.

This statement however, only evaluates the inner integral; is my approach correct?

I've got a function y(x) that is initially defined as x^3+y^3=1 and need to plot it, and find y',y''.

At present, I've used implicitplot(x^3+y^3=1,x=0..5,y=0..5) to plot it, but that doesnt seem to work. Also, to find y'

I've used the statement

implicitdiff(g(x,y),y(x),x) where g:=(x,y)->x^3+y^3=1 but this gives me an error that my input is invalid; y(x) is expected to be of the form {(name, set(name), set(function(name))}.

I don't quite understand..

I would like to know how to verify
y=x e5x cos(2x)
is a solution to the differential equation
y(4) -20 y”’+158 y”-580y’+841y=0

Dear All

I have a question:

How can I computet the laplace inverse of a function that is below!

My version of Maple is 13:

It should be noted that r>0, \rho>0.5, y\in R.

> restart;
> with(MTM);
print(??); # input placeholder
> ilaplace(r^(rho-.5)*abs(y)^(rho-1)*exp(-r*y)/GAMMA(rho-.5), s);

I need to plot the maximum of x^2 and sqrt(|x|) together on one graph. I've currently defined a procedure f that uses an if-else construct for the given function. However, when I use plot(f,-3..3); I get the following error:

"Warning, unable to evaluate the function to numeric values in the region; see the plotting command's help page to ensure the calling sequence is correct"

How do I resolve this error?

Hye, anyone know what is the float means?

and why maple cant gives the answer while the others software can?(for my problem)

hope anyone can help me because I really need this for my comparison study.

Here I have attached the file :.comparison_try1.mw

thank you in advance :)

Hello people in Mapleprimes,

I wish you to teach me about this.

From a matrix, I want to make a string.

pt3 := Matrix(4, 2, [1, 3, 4, 5, 6, 8, 5, 10]);

string1 := cat(

  "(", convert(pt3[1, 1], string), ",", convert(pt3[1, 2], string), ",", ")",

  "==",

  "(", convert(pt3[2, 1], string), ",", convert(pt3[2, 2], string), ",", ")",

  "==",

  "(", convert(pt3[3, 1], string), ",", convert(pt3[3, 2], string), ",", ")",

  "==",

  "(", convert(pt3[4, 1], string), ",", convert(pt3[4, 2], string), ")"

)

The above code makes 

string1 := "(1,3,)==(4,5,)==(6,8,)==(5,10)"

What I want to know is how to write a code of programming without writing each row of the above code.

Actually, though I wrote 4 row matrix above, the number of rows of matrix I want to deal with might be more than 100.

Best wishes.

taro

I am new to Maple. I am working though the manual and in chapter two I tried to get the derivative of ln(x^2+1). I am getting something completely different that the actual derivative. I tried a simple derivatie (the derivative of 2x and get 0). I do not know what I am doing wrong. Any help will be appreciated.