- #1
giokara
- 9
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Hello all,
I am searching for an analytic solution to an integral of the following form:
[itex]I[q',k\rho\,]=\frac{1}{\pi}\int_{0}^{2\pi}e^{jq'(\phi-\phi_0)}e^{-jk\rho\sin(\phi-\phi_0)}d\phi[/itex]
In this equation, [itex]q'[/itex] is real and [itex]k\rho[/itex] is real and positive.
Also, the following integral is closely related to the definition of Anger and Weber functions:
[itex]\frac{1}{\pi}\int_{0}^{2\pi}e^{jq'\phi}e^{-jk\rho\sin\phi}d\phi[/itex]
Although there seems to be a close link between both expressions, I am unable to transform [itex]I[q',k\rho\,][/itex] in order to use the known expression for the second integral. The reason is that the period of the exponential in the first expression is arbitrary, which does not allow a simple translation of the integrand. Has someone any ideas how to tackle this problem?
Lots of thanks in advance,
Giorgos
I am searching for an analytic solution to an integral of the following form:
[itex]I[q',k\rho\,]=\frac{1}{\pi}\int_{0}^{2\pi}e^{jq'(\phi-\phi_0)}e^{-jk\rho\sin(\phi-\phi_0)}d\phi[/itex]
In this equation, [itex]q'[/itex] is real and [itex]k\rho[/itex] is real and positive.
Also, the following integral is closely related to the definition of Anger and Weber functions:
[itex]\frac{1}{\pi}\int_{0}^{2\pi}e^{jq'\phi}e^{-jk\rho\sin\phi}d\phi[/itex]
Although there seems to be a close link between both expressions, I am unable to transform [itex]I[q',k\rho\,][/itex] in order to use the known expression for the second integral. The reason is that the period of the exponential in the first expression is arbitrary, which does not allow a simple translation of the integrand. Has someone any ideas how to tackle this problem?
Lots of thanks in advance,
Giorgos