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Student Support Forum: 'How to simplify this simple expression...' topicStudent Support Forum > General > Archives > "How to simplify this simple expression..."

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xavier
07/28/05 12:41pm

Hi,

Let p be a polynomial defined by :

p[y_] := Sum[Binomial[n + k - 1, k]*y^k, {k, 0, n - 1}]

For sure the equality :

((1 - y)^(-n))*(1-(y^n)*p[1-y]) == p[y]

is true for evry n>0.

but I not able to use mathematica to prove it.

If you try to Fullsimplify
((1 - y)^(-n))*(1-(y^n)*p[1-y]) - p[y]

you get a result using Hypergeometric2F1 and then mathematica seems not to be able to reduce this expression to 0 :(

Is there any way to help mathematica to find that
((1 - y)^(-n))*(1-(y^n)*p[1-y]) - p[y] is zero??


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Subject (listing for 'How to simplify this simple expression...')
Author Date Posted
How to simplify this simple expression... xavier 07/28/05 12:41pm
Re: How to simplify this simple expression... Henry Lamb 07/29/05 11:49pm
Re: How to simplify this simple expression... xavier 07/31/05 5:28pm
Re: How to simplify this simple expression... Henry Lamb 08/08/05 01:05am
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