31 Jul
2006
31 Jul
'06
12:43 p.m.
At 03:22 PM 7/29/2006, Henry Baker wrote:
Also, identities that allow asinh(x) to be computed recursively in terms of itself (shifts up or down).
Some easy identities from multiple angle (De Moivre) formulae with odd n: asinh(x) = asinh(3x+4x^3)/3 asinh(x) = asinh(5x+20x^3+16x^5)/5 etc. Even n produces cosh terms which can be replaced by cosh = sqrt(1+sinh^2) = sqrt(1+x^2), so they aren't polynomials. BTW, does anyone know if these polynomials belong to any "named" class of polynomials? Essentially equivalent are formulae based on the log expansion: asinh(x) = log(x+sqrt(1+x^2)) asinh(x) = log((x+sqrt(1+x^2))^n)/n