REGULAR FUNCTION ON THE BALL AND THE BICYLINDER IN QUATERNION CALCULUS
四元数分析中超球与双圆柱区域上的正则函数

in this paper, we obtain the Cauchy integral formulas of the regular quaternion functions on the ball and bicylinder, and prove the infinite differentiability of the regularquaternion fUnction on the general domain. Conditions for a quaternion function defined onthe boundary of the ball or the bicylinder to be able to be extended regularly into the inside ofthe domain are derived. We also discuss the Dirichlet and Neumann boundary value problemsfor the quaternion function F(z) satisfying the nonhomogeneous eqaution zF = f, and forthese problems have obtained the integral expressions of solutions on the ball and bicylinder.