recalling the formula tanh(x) + csch(2x) = coth(2x) = 1/tanh(2x) might help here. ----- Quoting françois mendzina essomba2 via math-fun <math-fun@mailman.xmission.com>:
Dear Pr. Gosper, following our last exchange. You did well to recall the very unusual nature of this continuous fraction that manages to be efficient in terms of calculations despite a theoretical convergence rate of zero. I admit that the formula that I transmitted to you in relation to tan (x) always intrigues me particularly.
Le Mardi 2 janvier 2018 23h58, françois mendzina essomba2 <m_essob@yahoo.fr> a écrit :
hello...
tanh(x) =-csch(2*x)+1/(-csch(4*x)+1/(-csch(8*x)+1/(-csch(16*x)+1/(-csch(32*x)+1/(-csch(64*x)+1/(-csch(128*x)+1/(?)))))));
approximation.
tanh(x)=-csch(2*x)+1/(-csch(4*x)+1/(-csch(8*x)+1/(-csch(16*x)+1/(-csch(32*x)+1/(-csch(64*x)+1/(-csch(128*x)+1/(1))))))); FME...
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