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

[Barton W. <wi...@un...>]

(%i5)    powerseries((1 + y )^ (1/n),y,0);
(%o5)    sum(y^i1/beta(i1+1,1/n-i1+1),i1,1,inf)/(1/n+1)+1



--Barton
________________________________
From: Susmita/Rajib <bkp...@gm...>
Sent: Wednesday, October 17, 2018 7:16:35 AM
To: max...@li...
Subject: [Maxima-discuss] Is there a way to expand ((1 + y )^ (1/n)) for y and n > 0?

Dear Illustrious Team Members, Maxima,

I tried with two inputs sequentially:

assume (y > 0, y < 1, n > 0);
expand ((1 + y )^ (1/n));

I don't get the Binomial expansion. The maxima manual has: expand ((x
+ y)^6); in the beginning of the manual. Which enticed me to try for a
variable (1/n) as a replacement for the constant 6.

The manual has in 10.3 Combinatorial Functions, a function called:
binomial (x, y) which is really an expression for combination ⁿCᵣ,
i.e., (n!)/(r!(n-r)!)
binomial (x, y) = x!/(y! (x - y)!)

Any advice in this regard? To have a binomial expansion of an
expression? I have a hunch that there is one. Otherwise, maxima
wouldn't be able to expand (x + y)^6).

Regards,
Rajib


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