## 60 Reputation

14 years, 245 days

## equality between two finite sums ...

Maple

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!

## Proof of an inequality...

Maple
 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

## Simplify a double sum ...

Maple

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

## explicit coefficient in a polynomial ...

Maple

Dear All,

We consider the polynomial

P(x)=(x+1)(x+2)...(x+n)

Question The Coefficient of x2 in Pn.

## Positivity of a finite double sum...

Maple
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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