Sunday, August 2, 2009

Regular function of quaternion variable

Because I explore calculus over division ring I put attention on different papers related to quaternion calculus. These papers mainly discuss definition of regular function. According to definition regular function is function which satisfy to differential equation


∂f/∂x0+i∂f/∂x1+j∂f/∂x2+k∂f/∂x3=0


Recently Daniel Alayon-Solarz sent me interesting example of regular function.

f(x0+x1i+x2j+x3k)=x0-x1i+x2j+x3k