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MaplePrimes Activity

These are questions asked by Chaggara

Let d and i two integers 


A := -(sum((-1)^k*binomial(i, k)*pochhammer(d*k+1, i), k = 0 .. i))/factorial(i)


B := (sum((-1)^k*binomial(i+1, k)*pochhammer(d*k+1, i+1), k = 0 .. i+1))/(d*factorial(i+1))

Question: Show that A=B


 Let d an integer ">=5 " and 
                    "lambda  in ]-(1)/(2),-(1)/(d+1)[. "
> gamma[s+1,d]=((s+1)[d]((d+1)lambda+s))/(2^(d+1)(lambda+s)[d+1]).;
We need to show that
> gamma[s+1,d]>=-(1)/(2^(s+1)),;
> s=1,...,[(d+1)/(2)].;
 a[k] designates the pochhammer symbol.

Thanks a lot 

Dear All 

I would like to calculate the five first terms of a  polynomial  sequence

I wrote in maple 

sum(x^r*(sum((-1)^s*binomial(r, s)*pochhammer((a+s+1)*d, n), s = 0 .. r))/factorial(r), r = 0 .. n), n = 0 .. 4);

I obtained 


which seems to be false

where is the problem 

Best regards 

Dear All,

We consider the polynomial 


Question The Coefficient of x2 in Pn.

If we consider the finite double sum I:=\sum{r=0}^{i}\sum{r=0}^{j}\frac{(-1)^k(i+j-r-s)! (\mu+\frac{1}{2})_{i+j-r-s}}{r!s!(i-r)!(j-s)!(k-r-s)!(\mu+\frac{1}{2})_{i-r}(\mu+\frac{1}{2})_{j-s}} where j positive integer j positive integer k positive integer such that 0\leq k\leq min(2i,2j) \mu a positive real Question: How we can use maple to justify that I is nonegative Thank you
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