## 385 Reputation

11 years, 112 days

## connection formulas for hypergeometric f...

Maple 18

Hello,

For instance consider the following exmple

restart;

hypergeom([a, b], [c], 1);

`assuming`([convert(%, GAMMA)], [c-a-b > 0])

it should be simplified to GAMMA functions, but I do not get maple to do it. Are there packages for this?

Same for higher functions pFq for example

hypergeom([1, 1, 2*q-2+L], [2, L+1], 1)

under appropriate assumptions.

## Collecting all terms (also if there are ...

Maple 2015

Hello,
I want to collect a function into terms without using ?expand() since this expands everything which I dont want.

f:=GAMMA(L+2*q-3-k)/(GAMMA(L-k)*k)*((GAMMA(-2*q+L)*GAMMA(L+2*q-3-k)-GAMMA(L+2*q-3)*GAMMA(L-2*q-1-k)*(L+2*k-1-(4*k+2)*q))/((2*(-1+2*q))*(4*q-3)*GAMMA(L+2*q-3)*GAMMA(L+2*q-3-k)));
collect(f,[k,GAMMA])

then has 1 term which still contains a denominator, but I want them seperate so I can use ?op() for all additive terms.

Is there an option without expanding the entire thing to enforce termwise selection?

Of course I could do it in a second step, but I want to avoid it and think it should be simpler.

## Numerical Round Off ?...

Maple 18

This is a follow up question to https://mapleprimes.com/questions/225877-Partial-Integration-Hint:

restart;

with(Physics, KroneckerDelta);

Digits := 15;

t4 := 1/3;

n := 4;

q := 4/7;

i1 := evalf(Int(t^n*exp(-t)*GAMMA(2*q-2, t*(1-t4)*(1/t4)), t = 0 .. infinity, method = _d01amc));

i2 := expand(simplify(GAMMA(2*q-2)*add(binomial(n, m)*(KroneckerDelta[m, 0]-GAMMA(3-2*q)*(1/GAMMA(3-2*q-m))*t4^m*(1-t4)^(2*q-2))*(-1)^m*factorial(n-m), m = 0 .. n)));

`~`[evalf]([op(i2)]);

i3 := expand(simplify(eval((-1)^n*GAMMA(2*q-2)*(diff((1-(1+t4*x*(1/(1-t4)))^(2-2*q))*(1/x), x\$n)), x = 1)));

`~`[evalf]([op(i3)]);

Interestingly this works up to n=3. It seems that the second term is wrongly manipulated and it should be 168/6 instead of 175/6?

I doubt the derivatives are wrong since I checked individually. I also hardly doubt this is a numerical round off, as the discrepancy is too large.

Is this a bug, or is there actually an error?

## partial integration hint?...

Maple 2018

Why can't maple integrate

restart;
`assuming`([int(GAMMA(a, s)*exp(-b*s), s = 0 .. infinity)], [b > 0, a > 0])

which has a simple result obtained by partial integration?

## Remove infinity from list...

Maple 18

How do I remove infinity from a list

s:=[f(x) , exp(a), GAMMA(2x)-1 , infinity , 1, -infinity]

remove(has,%,infinity)

does not work.

It should yield

s:=[f(x) , exp(a), GAMMA(2x)-1 , 1]

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