[math-fun] Incomplete Beta identity?
Bill and I just found this beta identity and don't recognize it: Beta[1-x,n,n]+Beta[x,n,n]==2^(1-2 n) Beta[1/2,n] --Neil Bickford
The two terms on the LHS sum to Beta(n,n). Then Beta(a,b) = Gamma(a) Gamma(b)/Gamma(a+b) and simple algebra give the identity. -- Gene
________________________________ From: Neil Bickford <techie314@gmail.com> To: math-fun <math-fun@mailman.xmission.com> Cc: Bill Gosper <billgosper@gmail.com> Sent: Thursday, June 16, 2011 5:03 PM Subject: [math-fun] Incomplete Beta identity?
Bill and I just found this beta identity and don't recognize it:
Beta[1-x,n,n]+Beta[x,n,n]==2^(1-2 n) Beta[1/2,n]
--Neil Bickford _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Thanks Gene, it's obvious by changing variables in one of the integrals. For the same reason: Beta[x, b, a] + Beta[1 - x, a, b] == Beta[a, b] for 0<x<1. --Neil Bickford On Thu, Jun 16, 2011 at 5:03 PM, Neil Bickford <techie314@gmail.com> wrote:
Bill and I just found this beta identity and don't recognize it:
Beta[1-x,n,n]+Beta[x,n,n]==2^(1-2 n) Beta[1/2,n]
--Neil Bickford
participants (2)
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Eugene Salamin -
Neil Bickford