Talk:Barnes G-function

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This page says that the G-function is a generalization of superfactorials, but the factorials page lists two kinds of superfactorials. What kind are we talking about? --Zemyla^t 03:29, 12 May 2006 (UTC)Reply

I think we should specify the superfactorial n$. Wilson868 (talk) 12:48, 26 May 2019 (UTC)Reply

No n$ means usually the exponential factorial and is not called superfactorial.

The superfactorial connected with the G-function is defined as the product 1! 2! 3! 4! ...(n-1)! n! 49.237.41.75 (talk) 16:23, 30 July 2022 (UTC)Reply

As far as I am aware, Barnes' orginal paper of 1900 is the only complete exposition in print of the theory of the G function. Could editors of this page please make sure that their amendments to this page agree with the original article? The article is extremely carefully written and repays careful study. I intend to add extra sections in the wikipedia article on integral representations of the G function, which so far have not been mentioned. The Barnes G function has assumed an unexpected importance since the mid 1960's after it was discovered that it appears naturally in the asymptotics of Toeplitz determinants and the closely related theory of random matrices. --Mathsci 17:16, 31 March 2007 (UTC)Reply

I agree, but when we spot errors we must correct them and not blindly copy formulas. In case of the asymptotic expansion, you can trivially verify that the formula you gave is wrong. In fact, why not numerically check the validity using Mathematica or Maple? That's exactly what I was doing when I spotted the error in the formula given by Adamchik. I then checked his paper again and found that he made a sign error.

I can easily reproduce the complete derivation from first principles here, if you want... Count Iblis 17:49, 31 March 2007 (UTC)Reply

For the record, it was not an error, just a mixup of conventions as Mathsci pointed out to me on my talk page. This will be explainedin the article. Count Iblis 18:22, 31 March 2007 (UTC)Reply

For the intervall [-2:-1] the function has negative values. For the intervall [-3:-2] the function has positive values. You can simply check this by applying the recurence formula backward, starting at 0.5 to -0.5, -1.5, -2.5, ... — Preceding unsigned comment added by 49.237.39.220 (talk) 18:32, 29 July 2022 (UTC)Reply

That's right. Here is how it looks like correctly.

I will replace the graphics in the article. Doc.Acid (talk) 12:10, 9 August 2022 (UTC)Reply

• Yup, the sign should alternate every 2 units rather than every 1. Thank you for catching that. Ovinus (talk) 13:53, 9 August 2022 (UTC)Reply

The reflection formula in terms of the Clausen function is obviously not correct for all ${\displaystyle z}$. It's correct at least for ${\displaystyle 0<z<1}$. If ${\displaystyle z}$ has a nonzero imaginary part then the analysis is probably more complicated. — Preceding unsigned comment added by ~2025-41088-26 (talk) 18:15, 16 December 2025 (UTC)Reply