I have the function of alpha + beta log(gamma((alpha+beta))), I want to calculate the derivative this function with respect to alpha. I need it as a derivative of inverted beta-liouville function with respect to each of its parameters.enter image description here

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    $\begingroup$ Can you work with a numerical approximation or do you need the actual analytical solution? If the numerical approximation is OK, doing a (cubic) spline interpolation for example can be much simpler to derive. $\endgroup$
    – PC1
    Jun 14 at 15:39
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    $\begingroup$ Welcome to MSE! Please learn to use MathJax so you can write formulas: math.meta.stackexchange.com/questions/5020/… $\endgroup$ Jun 14 at 15:50
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    $\begingroup$ The derivative of digamma is the trigamma function. Use the sum rule and chain rule to complete the solution. $\endgroup$
    – whuber
    Jun 14 at 15:59
  • $\begingroup$ You can use JAX to compute the derivatives: jax.readthedocs.io/en/latest/_autosummary/… $\endgroup$
    – Hyperplane
    Jun 14 at 16:59
  • $\begingroup$ @PC1 I actually need its general formula not as a values, cause I want to calculate the maximum likelihood with respect to each parameter $\endgroup$ Jun 14 at 18:42


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