I need to find value of g, such that zeta(g,1)/zeta(g) = K (where K is some numerical constant). I would like to be able to do this for a list of perhaps 40 values of K. zeta(g,n) is the nth derivative of the zeta function.
I am not familiar with this part of MATLAB, so I apologize for elementary question.
Dear Morton,
I wrote this example code for you:
clc
clear all
syms g f f_1
f=cos(g); % functiom
f_1=diff(f); % first derivative
x0=0;
% Convert symbolic expression to function handle
F1=matlabFunction(f_1/f);
K=[5.1 2 3 0.2]; % list K values
x=zeros(length(K),1);
for i=1:length(K)
F=@(g)F1(g)-K(i);
x(i)=fzero(F,x0); %solution vector
end
I can tell you in Maple it is Zeta(n, z). I know that matlab has a symbolic toolbox so probably you could find a link.
Thanks to the people for suggestions and hints.
Here is a way to use the symbolic processor, where g is the unknown and K = 0.273.
digits 5
syms g;
solx = solve(zeta(1,g)/zeta(g) == .273, g)
prints the solution of -2.8289
This got me thinking --- should this output be considered sensitive to small changes in the input? The answer (numerically) seems to be "no"... small changes in K make small changes in g.
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