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#
# besselzeros.m -- find zeros of bessel functions
#
# (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
#
global maxmu;
maxmu = 7;
global maxk;
maxk = 10;
global mu;
nachkommastellen = 4;
function retval = f(x)
global mu;
retval = besselj(mu, x);
endfunction
kzeros = zeros(maxk+1, maxmu+1);
for mu = (0:maxmu)
k = 0;
if (mu > 0)
kzeros(1, mu+1) = 0;
k = k+1;
endif
x = 0.0001;
while (k <= maxk)
bracket = [ x, x+1 ];
if (f(bracket(1)) * f(bracket(2)) < 0)
kzeros(k+1,mu+1) = fzero("f", bracket);
k = k + 1;
endif
x = x + 1;
endwhile
endfor
# kzeros
fn = fopen("besselzeros.tex", "w");
fprintf(fn, "\\begin{tabular}{|>{$}c<{$}");
for mu = (0:maxmu)
fprintf(fn, "|>{$}r<{$}");
endfor
fprintf(fn, "|}\n");
fprintf(fn, "\\hline\n");
fprintf(fn, " k ");
for mu = (0:maxmu)
fprintf(fn, "& \\mu = %d ", mu);
endfor
fprintf(fn, "\\\\\n");
fprintf(fn, "\\hline\n");
for k = (0:maxk)
fprintf(fn, " %d ", k);
for mu = (0:maxmu)
value = kzeros(k+1, mu+1);
if (value == 0)
fprintf(fn, "& 0\\phantom{.%0*d}", nachkommastellen, 0);
else
fprintf(fn, "& %*.*f", nachkommastellen+4, nachkommastellen, kzeros(k+1, mu+1));
endif
endfor
fprintf(fn, "\\\\\n");
endfor
fprintf(fn, "\\hline\n");
fprintf(fn, "\\end{tabular}\n");
fclose(fn);
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