[math-fun] True or False, Log[Tan[t + π/4]]
Taylor series about t = 0 has only odd powers and a rather long OEIS entry (A000364). -Veit
On Jul 27, 2016, at 6:35 PM, Bill Gosper <billgosper@gmail.com> wrote:
is an odd function of t? --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Shorter proof f(x) = log(tan(x + pi/4)) f(0) = 0 and f'(x) = 2 sec(2x) is even, hence f(x) is odd.
-----Original Message----- From: math-fun [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Veit Elser Sent: Thursday, July 28, 2016 12:44 AM To: math-fun Subject: Re: [math-fun] True or False, Log[Tan[t + p/4]]
Taylor series about t = 0 has only odd powers and a rather long OEIS entry (A000364).
-Veit
On Jul 27, 2016, at 6:35 PM, Bill Gosper <billgosper@gmail.com> wrote:
is an odd function of t? --rwg _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On Jul 27, 2016, at 6:35 PM, Bill Gosper <billgosper@gmail.com> wrote:
is an odd function of t? —rwg
The right question to ask, when it’s multivalued and analytic, is whether the Riemann surface has “odd symmetry”: (z1,z2) \in C^2 is on the surface iff (-z1,-z2) is on the surface. When this is true in an open neighborhood of the origin — as this case which has a regular Taylor series with only odd powers — then it holds for the entire Riemann surface by analytic continuation. -Veit
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Veit Elser