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| mjae Quote | Reply | | Integratiing exponentials posted on: 10/15/2006 5:08:40 AM Hi, I am trying to integrate exp(j*z*cos(x))*exp(j*z*a*cos(x)), where x= -infinity to +infinity). j is the complex number and z is a constant. Any suggestions apart from integrating by parts? Also, once the integration is done, does anybody have any tricks as to how to evaluate exponetial values with +infinity and -infinity apart from just doing it? thanks, Matthew. |
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Anomalies
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Integratiing exponentials
replied on: 10/15/2006 8:14:06 AM You can simplify your expression to exp[i z(1+a) Cos(x)] assuming that a is not equal to -1. I have tried to integrate this and I have failed. Mathematica cannot do it for me. So I think that this integral has no closed form in terms of elementary functions. Unless you have managed to get somewhere? |
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Mattywoo
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Integratiing exponentials
replied on: 10/29/2006 9:46:45 AM I haven't done complex calculus yet, so I don't know if there is anything special involved, but don't forget that cos(x) is simply Re(z). You can reduce the expression we wish to integrate to e^{(1+a)jz + Re(z)} which has many incarnations, such as {cos[(1+a)z] + jsin[(1+a)z]}.e^Re(z). All the best, Matt |
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Mattywoo
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Integratiing exponentials
replied on: 10/29/2006 9:54:05 AM Sorry scrap that there's a mistake there. The expression reduces to e^{(1+a)jz.Re(z)} which I imagine is not intergrateable because it's like trying to integrate [f(z)]^z dz. |
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