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Forcing a parameter to be integer when using 'Integrate'
*To*: mathgroup at smc.vnet.net
*Subject*: [mg67545] Forcing a parameter to be integer when using 'Integrate'
*From*: Ian Linington <i.e.linington at sussex.ac.uk>
*Date*: Fri, 30 Jun 2006 04:14:36 -0400 (EDT)
*Organisation*: University of Sussex, IT Services
*Sender*: owner-wri-mathgroup at wolfram.com
Hello,
I am a mathematica novice, so please excuse me if this question is a
bit dumb...
I would like to solve the integral:
> Integrate[E^((n*I)*x)/Sqrt[1 + a^2*Sin[x]^2], {x,0,2*Pi}]
with n integer and a real and positive.
The problem is that I don't know how to tell Mathematica about these
conditions on a and n.
If I explicitly assign an integer value for n (i.e. 4 in this example),
Mathematica solves the integral:
> Integrate[E^((4*I)*x)/Sqrt[1 + a^2*Sin[x]^2], {x,0,2*Pi}]
(with a few conditions) and gives the output
> If[(Re[a^(-1)] != 0 || -Im[a^(-1)] < 0) &&
(Re[a^(-1)] != 0 || -Im[a^(-1)] >= 0) && ...
... (lots more)...,
(4*(-8*(2 + a^2)*EllipticE[-a^2] +
(4 + a^2)*(4 + 3*a^2)*EllipticK[-a^2]))/(3*a^4),
Integrate[E^((4*I)*x)/Sqrt[1 + a^2*Sin[x]^2],
{x, 0, 2*Pi},
Assumptions -> !((Re[a^(-1)] != 0 || -Im[a^(-1)] < 0)
&& (Re[a^(-1)] != 0 || -Im[a^(-1)] >= 0) && ...)
... (lots more) ...]]
Simlilarly if we pick other integer values for n.
The question is, how to get a generic formula in terms of a and n?
Can anybody help please?
Many thanks,
Ian
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