mhill
Aug15-08, 10:58 AM
let be a quaternion a+ib+cj+dk and a,b,c,d are functions of (x,y,z,u)
my questions are.
- is there an anlogue of Cauchy integral theorem ?? , if an analytic function of a quaternion z , defined by f(z) , has a pole at the point 1+i+2j-3k How could you calculate its residue ??
- If a function of a quaternion is ANALYTIC does it satisfy \Box f =0
this would be a consequence that if Q is a quaternion (a,b,c,d) then
QQ^{*} = a^{2}-b^{2}-c^{2}-d^{2} * = conjugate , so QQ* is a real number.
i would be interested to find solution to integrals on 4 dimensions or to construct Laurent series for functions f(x,y,z,t)
my questions are.
- is there an anlogue of Cauchy integral theorem ?? , if an analytic function of a quaternion z , defined by f(z) , has a pole at the point 1+i+2j-3k How could you calculate its residue ??
- If a function of a quaternion is ANALYTIC does it satisfy \Box f =0
this would be a consequence that if Q is a quaternion (a,b,c,d) then
QQ^{*} = a^{2}-b^{2}-c^{2}-d^{2} * = conjugate , so QQ* is a real number.
i would be interested to find solution to integrals on 4 dimensions or to construct Laurent series for functions f(x,y,z,t)