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Quaternion calculus.

  1. Aug 15, 2008 #1
    let be a quaternion [tex] a+ib+cj+dk [/tex] 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 [tex] \Box f =0 [/tex]

    this would be a consequence that if Q is a quaternion (a,b,c,d) then

    [tex] QQ^{*} = a^{2}-b^{2}-c^{2}-d^{2} [/tex] * = 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)
  2. jcsd
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