Talk:Inverse gamma function

Missing Explanation

In the Approximation section, what does \Psi mean in \Psi\left(1,\ \alpha\right)? Other notations, such as the Lambert W function are explained, just not this one. Sudleyplace (talk) 19:01, 28 April 2025 (UTC)

I am fairly confident that it is the digamma function. But I don't know this particular equation, so I can't be sure. —Quantling (talk | contribs) 19:27, 28 April 2025 (UTC)

But the digamma function takes one variable, this one takes two. Possibly Multiple gamma function ? Sudleyplace (talk) 15:15, 29 April 2025 (UTC)

Thank you, I agree that the digamma function takes only one parameter. There can be two parameters when describing a gamma distribution, so I suppose it is possible that this article's Ψ is somehow a derivative of that probability density function with respect to one of its parameters. But in short, I just don't know. ☹ —Quantling (talk | contribs) 16:10, 29 April 2025 (UTC)

Not really. It’s actually the trigamma function, or $\psi ^{(1)}(x)$. If you don’t believe me, you can evaluate the approximation with $\Psi (1,x)=\psi ^{(1)}(x)$ in some graphing calculator like Desmos to see for yourself. In fact, I already decided to make the graph: https://www.desmos.com/calculator/dxagxahiek Keep in mind that $T(x)=\psi ^{(1)}(x)$ in the graph and that later values won’t be accurate due to it coming from a Taylor series. 107.9.36.50 (talk) 20:11, 5 May 2025 (UTC)