Mma prefers Pi/8 + ArcCot[2] + ArcCot[3]/2 ----- Original Message ----- From: "R. William Gosper" <rwg@spnet.com> To: <math-fun@mailman.xmission.com> Sent: Monday, February 24, 2003 9:17 PM Subject: Re: [math-fun] identity from a stranger
Assuming he(?) means inf ==== k 1 \ 1 1 2 1 - > (- -) (----------- + ------- + -------), 2 / 4 2 (4 k + 3) 4 k + 2 4 k + 1 ==== k = 0
my Macsyma series package gets atan(2)/2 + atan(1/2), as would Maple and Mma, presumably. It isn't hard to show this is atan(phi), but neither is it an obvious simplification. --rwgOC
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