Tokoro

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These are answers submitted by Tokoro

 

Number of mesh, node x, node y; n, px, py
 

 

 

with(plots):
a:=[n,0]:b:=[0,n]:
ptsx:=[seq([0,j],j=0..n)]:
ptsy:=[seq([i,0],i=0..n)]:
linesx:=map(o->([o,o+a],[o,o]),ptsx):
linesy:=map(o->([o,o],[o,o+b]),ptsy):

plotlinesx:=display(map(x->plottools:-line(x[]),linesx),color=blue,linestyle=solid,thickness=3,axis = [tickmarks = [n, subticks = 0]]):
plotlinesy:=display(map(x->plottools:-line(x[]),linesy),color=blue,linestyle=solid,thickness=3,axis = [tickmarks = [n, subticks = 0]]):
Google2D := proc(m, n) local Gans; Gans := 1/2*int((1 - ((x - 1)/(x + 1))^(n + m)*((x - I)/(x + I))^(m - n))/x, x = 0 .. infinity)/Pi; return Gans; end proc:

NULL

 

 

 

Google2D(1,2)

(1/2)*(8-Pi)/Pi

(1)

Google2D(3,3)=46/(15*Pi)

 

(2)

display([plotlinesx, plotlinesy], pointplot([[(1/2)*n, (1/2)*n], [(1/2)*n+px, (1/2)*n+py]], color = red, symbol = solidcircle, symbolsize = 20), view = [0 .. n, 0 .. n])

 

NULL

 

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