(HP-67) Barkers's Equation

[Mathias Zechmeister]

Thanks for the reference. So the relation is mathematically known, but it was likely not applied to Barker's equation.

With the relation:

(12-06-2019 06:39 PM)Albert Chan Wrote:  x = 2 sinh(sinh^-1(W)/3)

it is even simplier to compute Barker's equation with a pocket calculator than in R. Meire (1985).
Well, it seems the HP-67 had no hyperbolic functions.

I'm working on a follow-up paper of Zechmeister (2018) and I'm going to mention this relation.

(04-11-2020 03:29 AM)Albert Chan Wrote:  Another way is with identity: sinh^-1(z) = ln(z + √(z²+1))
→ y = e^(sinh^-1(W)/3)
→ x = 2 sinh(sinh^-1(W)/3)

Indeed, that is, how I found it. I noted the term z + √(z²+1) in Barker's equation, and Fukushima (1997, Eq. 73) as well as Raposo-Pulido+ (2018, Eq. 43) reminded of this identity.