[Maxima-discuss] Fwd: Is there a way to expand ((1 + y )^ (1/n)) for y and n > 0?

[Stavros M. (Σ. Μ. <mac...@al...>]

Just because you call it an "expansion" doesn't mean that the "expand"
command performs this operation. Read the fine manual (? expand). "Expand"
will expand products and integer exponentials. It does not "expand"
symbolic or fractional exponentials.

I think what you want is either "taylor" (which gives n terms) or
"powerseries", which gives a general expression (as Barton Willis has
already pointed out):

ex: (1+x)^(1/n);

taylor(ex,x,0,4);

       1 + x/n - ((n-1)*x^2)/(2*n^2) + ((2*n^2-3*n+1)*x^3)/(6*n^3) -
((6*n^3-11*n^2+6*n-1)*x^4)/(24*n^4) + ...

powerseries(ex,x,0);

      ('sum(x^i1/beta(i1+1,1/n-i1+1),i1,1,inf)) / (1/n+1) + 1

If you are unfamiliar with the beta function, you can google it.

On Thu, Oct 18, 2018 at 11:22 PM Susmita/Rajib <bkp...@gm...>
wrote:

> Good afternoon, Sir.
>
> Is my version of maxima creating a problem? Because I can't expand.
>
> I wanted a form like the link below —  the usual Binomial Equation
> with summation notation usually come across in books on the LHS — to
> the un-compacting of all terms (i.e., n+1 terms) for any y and
> integral n. Also, the infinite terms truncated to, say 10 terms, for n
> as rational and |y| <1.
>
> Like this expanded form.
>
>
> https://gradestack.com/JEE-Main-2015-Complete/Binomial-Theorem/Binomial-Theorem-for-Any/19662-4056-42813-study-wtw
>
> =================================================
>                                 My input outputs are as follows:
> =================================================
> /* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
> /* [ Created with wxMaxima version 12.04.0 ] */
>
> /* [wxMaxima: input   start ] */
> assume ( 0 < y , y < 1, n > 0);
> eq1 = ((1 + y )^ (1/n));
> /* [wxMaxima: input   end   ] */ working
>
> /* [wxMaxima: input   start ] */
> subst( n=10, %o2 );
> /* [wxMaxima: input   end   ] */ working
>
> /* [wxMaxima: input   start ] */
> expand((%o3));
> /* [wxMaxima: input   end   ] */ fails. Returns same o3.
> =================================================
>
>                                 OR
>
> =================================================
>                                 Alternatively:
> =================================================
> /* [wxMaxima batch file version 1] [ DO NOT EDIT BY HAND! ]*/
> /* [ Created with wxMaxima version 12.04.0 ] */
>
> /* [wxMaxima: input   start ] */
> assume ( 0 < y , y < 1, n > 0);
> ((1 + y )^ (1/n));
> /* [wxMaxima: input   end   ] */ working
>
> /* [wxMaxima: input   start ] */
> subst( n=10, %o2 );
> /* [wxMaxima: input   end   ] */  working
>
> /* [wxMaxima: input   start ] */
> expand((%o3));
> /* [wxMaxima: input   end   ] */  fails. Returns same o3.
> =================================================
>
> Neither of the 3rd step, expand((%o3)); , works for my version.
>
> Am I going wrong anywhere?
>
> Regards,
> Rajib
>
>
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