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Help me please to apply a Laplace-like operator:$ \Delta f:= \frac{\partial^2 f}{\partial r^2} + \frac{\partial^2 f}{\partial z^2} + {1\over r}\,\frac{\partial f}{\partial r} - {f\over r^2} $ on the expression: $f:=\frac{r}{a}\rho^{-\alpha}\sin (\alpha\phi)$.

when $\rho=\sqrt{(r-a)^{2}+z^{2}} $

Thanks a lot!

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    Did you m$a$n$a$ge to solve the problem?2012-10-07

1 Answers 1

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You can use MATLAB Program :

   syms r a z alpha phi     rho=sqrt((r-a)^2+z^2);    f=(r/a)*rho^(-alpha)*sin(alpha*phi);    delta_f=diff(f,r,2)+diff(f,z,2)+(1/r)*diff(f,r)-f/(r^2);    delta_f=simple(delta_f);    pretty(delta_f) 

$ \Delta f:= \frac{\partial^2 f}{\partial r^2} + \frac{\partial^2 f}{\partial z^2} + {1\over r}\,\frac{\partial f}{\partial r} - {f\over r^2} $ $ \Delta f := \frac{\alpha \space sin (\alpha \phi) (3a -3r+r \alpha)}{\alpha (a^2-2ra+r^2+z^2)^{\frac{\alpha}{2}+1}} $