Here below my program. I would like to calculate the taylor approximation of R near kx0. and woul like to calculate the sum of sigma power n.
It works well but for order more than3 doesn't work . Furthermore, for some values of theta doesn't work and displays the error you find here.( for a value of theta + 1.58, it dosn't displays this error).
Any one has an idea??
Thank you in advance!
Adam
clear all;lambda=3E-6; k1=2*pi/lambda; n=3.42; theta=((asin(1/n))*180)/pi;w0=10E-3; k2=k1/n;q=1; syms kx sigma u kx0=k1*sin(theta);sigma=-(kx-k1.*sin(theta))./(k1.*cos(theta));R=((k1^2-kx^2)^(1/2)-q*(k2^2-kx^2)^(1/2))/((k1^2-kx^2)^(1/2)+q*(k2^2-kx^2)^(1/2))% Reflectance R
syms kx sigma u cleart1=taylor(R,kx,kx0,'Order', 1)p=symsum(sigma^u, u, 0, 0)Bn=t1./pvall=subs(R,kx0)val1=subs(t1,kx0)val2=subs(p,kx0)val3=subs(Bn,kx0)val4=val1/val2Error using mupadmexError in MuPAD command: Cannot compute a Taylor expansion of -((1536119361583697/4096 - kx^2)^(1/2) -(8983533250413779/2048 - kx^2)^(1/2))/((1536119361583697/4096 - kx^2)^(1/2) + (8983533250413779/2048 - kx^2)^(1/2)).Try 'series' for a more general expansion. [taylor]Error in sym/taylor (line 142) tSym = mupadmex('symobj::taylor',f.s,x.s,a.s,options);Error in reflexiontotale2 (line 19)t1=taylor(R,kx,kx0,'Order', 1)
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