Thank you - but how you see it?

May be all that follows also in greater generality from Gautschi, 
Orthogonal Polynomials - Computation and Approximation (2004),
2.1.8.2 Conversion algorithm, p. 80 ff.

However I have not checked it ...

May be all that follows also in greater generality from Gautschi, 
Orthogonal Polynomials - Computation and Approximation (2004),
2.1.8.2 Conversion algorithm, p. 80 ff.

However I have not checked it ...

Almost what I wanted to see (besides accessing to www page, not the locally stored one (*)) and the only thing i would miss here is the summary in the last line of that table abd the info "Data for dd mmm yyyy" at the beginning of the page.

(*) is it possible to do that parametric request?

agree with acer & would like to see how to extract something like below (for which I use(d) Excel):

www.eurexchange.com/market/statistics/market_statistics/online.html

Alec,

Thank you for this!

Though I found no source the problem seems to by named "finding connection coeffcients" and in W. Koepf, D. Schmersau "Representations of orthogonal polynomials" [Journal of Computational and Applied Mathematics 90 (1998) p 57-94] there are given some references (also classical ones like Szegö, however I did not had look up those).

Axel

link to that paper: www.mathematik.uni-kassel.de/~koepf/represent.pdf

Edited to add: the other stuff I found was Matlab code cheb2leg.m from 2004 and since I do not speak that tried the converter with(Matlab) - however the result in Maple is almost unreadable for me (thus did not try to check whether it is numerical usefull or sound).

Alec,

Thank you for this!

Though I found no source the problem seems to by named "finding connection coeffcients" and in W. Koepf, D. Schmersau "Representations of orthogonal polynomials" [Journal of Computational and Applied Mathematics 90 (1998) p 57-94] there are given some references (also classical ones like Szegö, however I did not had look up those).

Axel

link to that paper: www.mathematik.uni-kassel.de/~koepf/represent.pdf

Edited to add: the other stuff I found was Matlab code cheb2leg.m from 2004 and since I do not speak that tried the converter with(Matlab) - however the result in Maple is almost unreadable for me (thus did not try to check whether it is numerical usefull or sound).

usually one can save the page as html, then they appear as text

Thank you: yes, I have it loaded for handy use of 'changevar' and will try again tonight without that

Edited: yes, not loading that package makes it work for me as well.

Thank you: yes, I have it loaded for handy use of 'changevar' and will try again tonight without that

Edited: yes, not loading that package makes it work for me as well.

That does not work for, for your example I get "Error, (in Sum) Usage: Sum(expr,name) or Sum(expr,name=a..b) or Sum(expr,name=RootOf(...))"

That does not work for, for your example I get "Error, (in Sum) Usage: Sum(expr,name) or Sum(expr,name=a..b) or Sum(expr,name=RootOf(...))"

My answer would have been (but as acer is much faster, so I did not post it):

It depends a bit on the notations you are using and whether
that homework is Math or using Maple for it (or both).

For the Math recall the formula Int( norm(D(f)(t)) , t= 0 ... 1)
if f is a parametrization over the unit interval and D(f) means
(componentwise) differentiation. Here norm stands for the usual
Euclidean norm, i.e. sqrt summing squares of components (it does
not matter, if you have a different interval for parametrization,
the lecture should tell you that).

Following the hint for the plot given try to figure out by paper
and pencil the integral which has to be computed.

Look up the help how Maple does numerical and symbolical integrals.

Type in what you have (avoiding typos) and you are done, your
result should be ~ 9.86 (Maple will give a symbolic, exact result).

If you can not manage it, then come back and tell, what you have
done and what you have achieved - or what are your problems.

Without that and honesty it is unlikely you get more help ...

On the other side I consider his answer quite fair: if Maple would have a reasonable search
within the help that might be given through through that ...

My answer would have been (but as acer is much faster, so I did not post it):

It depends a bit on the notations you are using and whether
that homework is Math or using Maple for it (or both).

For the Math recall the formula Int( norm(D(f)(t)) , t= 0 ... 1)
if f is a parametrization over the unit interval and D(f) means
(componentwise) differentiation. Here norm stands for the usual
Euclidean norm, i.e. sqrt summing squares of components (it does
not matter, if you have a different interval for parametrization,
the lecture should tell you that).

Following the hint for the plot given try to figure out by paper
and pencil the integral which has to be computed.

Look up the help how Maple does numerical and symbolical integrals.

Type in what you have (avoiding typos) and you are done, your
result should be ~ 9.86 (Maple will give a symbolic, exact result).

If you can not manage it, then come back and tell, what you have
done and what you have achieved - or what are your problems.

Without that and honesty it is unlikely you get more help ...

On the other side I consider his answer quite fair: if Maple would have a reasonable search
within the help that might be given through through that ...

Just a sketch (had an ugly working day), may be helps (as I do not
quite understand where your problems are ... just have a break?).

  h:=hypergeom([-1/2*p, 1/2*p+1/2],[1/2],x^2);
  convert(%,FormalPowerSeries,x=0,dummy=k); convert(%,GAMMA);
  op(1,%); 
  subs(x=1,%); # <-----------
  a:=unapply(%,k);

                                                           k
                    GAMMA(- p/2 + k) GAMMA(p/2 + 1/2 + k) 4
        a := k -> --------------------------------------------
                  GAMMA(- p/2) GAMMA(p/2 + 1/2) GAMMA(2 k + 1)


Then (here) your have h = Sum(a(k)*x^k, k=0 ... infinity), *as far as
that converges* (which is true for |x| < 1 at least, see below).

  a(k)/a(k-1); simplify(%): [numer(%),denom(%)]: collect(%,k): %[1]/%[2];

                       2
                    4 k  - 6 k + (-2 - p) (-1 + p)
                    ------------------------------
                                 2
                              4 k  - 2 k

Note: if h *is* a polynomial, then you can not write down the quotient
(division by 0) and that will be the case if p = multiple of 2 (or so),
this is is a general assumption in the criterion ...

Otherwise you can consider the limit

  limit(%,k=infinity);
                                  1

This is proved in Analysis 1 (and told at school without proof ~ 11th
class ~ 17 years) for rational functions, so either I missunderstood
your problem ... or you just need some coffee break :-)

But if it is a polynomial, then the series terminates and it will
converge in the plane.

Note the formula for a(k) and p = even causes formal problems, since
Maple works with GAMMA and unfortunately not with 1/GAMMA (so you will
need assumptions already there, which Maple does not tell you), you
may heal it through limits (or: look at pochhammer before GAMMA).