Generalization of the unity of higher-order derivatives and original functions of complex special functions

higher-order derivatives;  Original function;  uniformity;  Promotion

The unified formula of the higher-order derivative and the original function studied in literature [1] is extended to the special function with a more complex structure by mathematical induction, and more widely used results than those in literature [1]. The results show that the inverse operation of the higher-order derivative and the original function can be unified in some complex special functions. By using this result, you only need to analyze the derivative of this complex special function and its own structural characteristics, and you can quickly obtain the results of the higher-order derivative and original function representing the complex special function with the same formula without analysis.