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How do I find poles and zeroes from this complex transfer function?

$$ H(s) = \frac{2959}{100\,s} - \frac{ 171\, \Gamma\left( \frac{7447}{10000} \right)} {200\, s^{7447/10000}} $$

I used the Laplace transform function in MATLAB and am trying to create a Bode plot using other functions. I believe if the order of a pole is not integer (1, 2, 3, ...) then I can't plot this with MATLAB's built-in functions, but can use another integrated toolbox like FOMCON available in MATLAB.

I searched online and I found that I could use the FOMCON toolbox, but I need to properly convert this into a form where I can find poles and zeroes; then I can provide input to the tool to create the Bode plot. Can anyone advise?

enter image description here

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    \$\begingroup\$ bleh it's just a fractional power. For some techniques like Root Locus or Nyquist, it can be approximated into several poles and zeros (over a particular range of frequency that would be chosen to be useful), for example by Padé Approximant. Alternatively, stuff like Bode plot can be done with no modification at all, the slope of the line on the gain plot is just fractional, and the phase is just a fractional multiple of pi/2 \$\endgroup\$
    – Pete W
    Commented Feb 6 at 1:51
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    \$\begingroup\$ Matlab should have a Pade function. Read the docs, because you need to give it a couple of parameters ......... update. evidently there's a Fractional Order Toolbox now for matlab . Probably that's a better way to go \$\endgroup\$
    – Pete W
    Commented Feb 6 at 1:53
  • \$\begingroup\$ I believe if order of pole is not integer (1,2,3..) then I can't plot this in matlab. Are you sure about that? You could just manually make the Bode plot in matlab, without using the built-in function. \$\endgroup\$ Commented Feb 6 at 2:25
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    \$\begingroup\$ Im just using wolfram to convert into the proper format to read off poles and zeros location.. wolframalpha.com/… I've looked at pade function but how is this relevant? I am using fractional toolbox from matlab so i have no issue wiht it. Just needed proper conversion \$\endgroup\$
    – igor
    Commented Feb 6 at 2:43

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The function has a pole at the origin which is also an infinite branch point.

enter image description here

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