Re: Positive Integer Assumptions
- To: mathgroup at smc.vnet.net
- Subject: [mg43774] Re: Positive Integer Assumptions
- From: bobhanlon at aol.com (Bob Hanlon)
- Date: Sat, 4 Oct 2003 02:04:53 -0400 (EDT)
- References: <blj5ra$1gi$1@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
f[x_,n_,m_]:=n!/((n-m)!(m-1)!) x^(m-1) (1-x)^(n-m)
Use Assumptions
Integrate[x^k * f[t,n,m],{t,0,x},
Assumptions->{Element[{k,n,m}, Integers],
k >0, n >0, m >0, 0<x<1}]
(120*x^(k + m)*Hypergeometric2F1[m - 5, m, m + 1, x])/
(m*(5 - m)!*(m - 1)!)
Although fewer assumptions can be used
Integrate[x^k * f[t,n,m],{t,0,x},
Assumptions->{m >0, 0<x<1}]
(120*x^(k + m)*Hypergeometric2F1[m - 5, m, m + 1, x])/
(m*(5 - m)!*(m - 1)!)
Or turn off GenerateConditions
Integrate[x^k * f[t,n,m],{t,0,x},
GenerateConditions->False]
(120*x^(k + m)*Hypergeometric2F1[m - 5, m, m + 1, x])/
(m*(5 - m)!*(m - 1)!)
Table[%, {m,8}] // Simplify
{x^(k + 1)*(x^4 - 5*x^3 + 10*x^2 - 10*x + 5),
x^(k + 2)*(-4*x^3 + 15*x^2 - 20*x + 10),
x^(k + 3)*(6*x^2 - 15*x + 10), (5 - 4*x)*x^(k + 4),
x^(k + 5), 0, 0, 0}
Bob Hanlon
In article <blj5ra$1gi$1 at smc.vnet.net>, Stewart Mandell <stewart at rentec.com>
wrote:
<< How do I specify assumptions that k,n,m are all positive integers in the
Integral
f[x_, n_,m_] := n!/((n-m)!(m-1)!) x^(m-1) (1-x)^(n-m)
Integrate[ x^k f[t, n, m], {t, 0, x}]