The method of separation of complex variable and the real principle in mathematical physics are suggested to solve the problem of partial deferential equations， which have odd order cross derivatives and the background of anisotropic physics， in Cartesian， skew， cylindrical and spherical coordinates. Several complex special functions to solve anisotropic mathematical physics equation are developed， It is noted that the many special functions are orthogonal with particular weight over particular domain and these corresponding complex cylindrical and spherical functions expansion theorems are also suggested. In solving the problem of isotropic physics equation some complex special functions in cylindrical coordinates can be reduced to the corresponding Bessel functions respectively. The author conducted a systematic study of some complex special functions. By these complex special functions， many analytical solutions for the problems of anisotropic physics are presented .The anisotropic wave equations are solved by the method of separation of complex variable and the complex special functions. The series of complex cylindrical function transforms are also developed and several complex function transforms are presented. The basic properties and tables of complex cylindrical function transform are also presented. For the problem of isotropic physics， the complex cylindrical function transform is reduce to Hankel Transform.
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