  Six years after William Rowan Hamilton's discovery of quaternions, in 1849
James Cockle introduced the algebra of split quaternions. (He called them
``coquaternions.'') In this paper we define regular functions on split
quaternions and prove two different analogues of the Cauchy-Fueter formula for
these functions.
  In the paper "Split quaternionic analysis and the separation of the series
for SL(2,R) and SL(2,C)/SL(2,R)" joint with Igor Frenkel we naturally apply the
methods and formulas of quaternionic analysis to solve the problems of harmonic
analysis on SL(2,R) and the imaginary Lobachevski space SL(2,C)/SL(2,R).
