Let d and i two integers 

Put 

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

and 

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

Thanks!

 Let d an integer ">=5 " and 
                    "lambda  in ]-(1)/(2),-(1)/(d+1)[. "
Put
> 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)),;
for 
> 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 

0,0,0,0,0

which seems to be false

where is the problem 

Best regards 

Dear All,

We consider the polynomial 

P_n (x)=(x+1)(x+2)...(x+n)

Question The Coefficient of x² in P_n.

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