[math-fun] asinh (hyperbolic arc sine) identities ?

Hyperbolic arc sine function is an interesting function which is 1-1, linear at the origin and logarithm towards +-oo. I'm looking for interesting identities involving this function. In particular identities for things like asinh(sinh(x)+c), c constant asinh(sinh(x)*c), c constant asinh(sinh(x)+sinh(y)) asinh(asinh(x)*asinh(y)) Also, identities that allow asinh(x) to be computed recursively in terms of itself (shifts up or down). If these don't work so well, then identities involving acosh or atanh, but neither of these functions are particularly interesting due to their reduced domains.