Mathematics was first developed in counting, and algebraic equations were formed by the combination of addition, subtraction, multiplication, division and idempotency between numbers and unknowns: linear equations in one variable, quadratic equations in one variable, linear equations in two dimensions and so on. However, with the emergence of the concept of function and the introduction of differential and integral operation based on function, the category of equation is wider, and the unknowns can be mathematical objects such as functions and vectors, and the operation is no longer limited to addition, subtraction, multiplication and division.

Calculus is a branch of mathematics, which studies the differential and integral properties of functions and their applications. It has become the foundation of other branches of mathematics, and it is also an essential tool for other natural sciences and engineering technology.

Equation occupies an important position in mathematics and seems to be an eternal topic in mathematics. The appearance of equations not only greatly expanded the application scope of mathematics, but also solved many problems that could not be solved by arithmetic problem-solving methods, which had a great influence on the progress of mathematics later. In particular, many important discoveries in mathematics are closely related to it.

Using power series as a tool, the function theory is expanded through strict pure analytical reasoning. Analytic function is defined as a function that can be expanded into power series, and the properties of function are studied around singularity.

Different from the above equation, the unknown in the equation is the function itself, not the independent variable of the function; Operations involve addition, subtraction, multiplication, division and function synthesis.