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I am thinking about buying Maple, but I would like to know how it does with the following problem:

f(x):=log(2-cos(x)+sqrt(3+cos(x)*(cos(x)-4))) ;
r(n,p):=(1/%pi)*integrate((1-exp(-abs(n)*f(x))*cos(p*x))/sinh(f(x)),x,0,%pi) ;
r(1,3) ;


These are Maxima commands--let me know if it is not clear what they are doing.  I am wondering if someone with Maple could translate these commands into Maple-ese and try them. (Maxima just gives up on this integral.)

r(n,p) is the resistance between node (0,0) and node (n,p) in an infinite square lattice of 1-ohm resistors.  Here are the exact symbolic answers you should get for a few nodes:

r(0,1)=0.5

r(1,1)=2/pi

r(1,3)=-4+46/3pi   (This is the one given above)

r(2,5)=(97/2)-(2236/15pi)

These answers were gotten with Mathematica, but Mathematica is too expensive for me (they won't sell the student version to a retired electrical engineer pursuing math studies as a hobby).

Thanks,

Bob Baker

 

 
integral

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