Hi,(adsbygoogle = window.adsbygoogle || []).push({});

I am new here, but apparently there are some decent mathematicians around, so I would like to confront you with a double integral problem.

Consider

[tex] \psi_n(z) = \int_0^{2\pi}\int_0^1 \frac{ (z-\frac{1}{2}) \cdot (r \cos(\theta) + \frac{1}{2})^n \cdot r} { \sqrt{ 4z^2+4r^2+4r\cos(\theta)+2-4z }^(2n+3) }\,dr\,d\theta [/tex]

which is a function of z for given n, n>0.

The problem is that I need an analytical sloution, because \psi_n shall be integrated again which can then be done numerically. I considered basic integration methods and gave the expression to maple but it didn't help. I wonder if there is any possibility to simplify the integrand / solve the integral.

If you don't think so please tell me so, too, this would already be some help. Thank you.

Hendrik

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# Complicated Double Integral

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