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According to the last paragraph in Mathworld's Beta function article http://mathworld.wolfram.com/BetaFunction.html, Gosper found some multiplication formulas for the Beta function, but it does not tell us where to find them. It is not hard to prove these identities using the multiplication formula for the Gamma function, but I would like to cite them.

Does anyone know where can I find a (hopefully published) reference for these identities?

I did a search on mathscinet and google but found nothing, except for an unpublished letter from Gosper to Stanton, which maybe states these formulas.

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    $\begingroup$ Why not ask Bill Gosper directly? His web site lists a snail mail address... Many of his formulas are listed in On some strange summation formulas, but I did not find the beta function identity there. $\endgroup$ – Carlo Beenakker Dec 31 '18 at 22:31
  • $\begingroup$ Thank you very much @CarloBeenakker, as always. I will wait a little, and if there are no responses, I will contact Professor Gosper. $\endgroup$ – EFinat-S Dec 31 '18 at 23:06

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