hgb>I'm still looking for good formulae for the following cases:

sinh(x*2^k) = ?? sinh(x+y) = ?? Well, as Joshua suggests, n n ==== /===\ \ k | | %i %pi k %i > (- 1) | | 2 %i sinh(-------- + a ) n / | | n + 1 j ==== ==== j = 0 \ k = 0 sinh( > a ) = - ---------------------------------------------- / k 2 n + 2 ==== k = 1

(with the fast stable recurrence still an option, and the prod becoming a power for a[k]:=x.) But sinh(i pi/2 +a) = i cosh(a), so I guess that's not your pleasure either.

asinh(x*2^k) = ?? asinh(x+y) = ??

A special case of both of these is asinh(2*x), but all I see is 2 asinh(sqrt(x - 1) + x) = asinh(sqrt(x)) + asinh(sqrt(x - 1)). --rwg __________________________________________________ Do You Yahoo!? Tired of spam? Yahoo! Mail has the best spam protection around http://mail.yahoo.com