Add some more properties of log minus digamma function

[yousuketakada]

• [x] Positivity from the comparison between the log expectation and the logarithm of the mean of the gamma-distributed random variable, making use of Jensen's inequality.
• [ ] Define complete monotonicity.
• [ ] Asymptotic expansion of the log gamma function.
• [ ] Complete monotonicity of the residual of the asymptotic expansion.
• [ ] Complete monotonicity of the log minus digamma function.
• [ ] Log minus digamma function is convex ($a_{\text{ML}}$ indeed maximizes the likelihood).
• [ ] Log minus digamma function is bijective and thus invertible.
• [ ] Numerical solution for the inverse of the log minus digamma function.
• [ ] Add figure for log minus digamma function.