Formal holomorphic function
Formal holomorphic functions are like pretend functions that only exist on paper. They are a special kind of function that you can write down with just some numbers and variables, but they might not actually work when you try to plug in real numbers for the variables.
Imagine you are trying to draw a picture of a cake on a piece of paper, but you don't have any crayons or markers to color it in. So instead, you use a bunch of symbols like circles and squares to represent the different parts of the cake. You might write down something like "cake = circle + rectangle." You know that you can't actually eat or taste the cake from the picture you drew, but it helps you understand how the parts fit together.
It's the same with formal holomorphic functions. They are like a recipe or a blueprint of a function, written down as a series of symbols and variables. You can use them to understand how the function behaves in a theoretical sense, but they might not actually work when you try to plug in real numbers.
The word "holomorphic" means that the function is very smooth and nice, without any bumps or jumps in it. Like how a very smooth cake batter is easier to work with than a lumpy one. So a formal holomorphic function is like a pretend batter that is perfectly smooth and easy to work with, even if you can't taste it or use it to make a real cake.
Imagine you are trying to draw a picture of a cake on a piece of paper, but you don't have any crayons or markers to color it in. So instead, you use a bunch of symbols like circles and squares to represent the different parts of the cake. You might write down something like "cake = circle + rectangle." You know that you can't actually eat or taste the cake from the picture you drew, but it helps you understand how the parts fit together.
It's the same with formal holomorphic functions. They are like a recipe or a blueprint of a function, written down as a series of symbols and variables. You can use them to understand how the function behaves in a theoretical sense, but they might not actually work when you try to plug in real numbers.
The word "holomorphic" means that the function is very smooth and nice, without any bumps or jumps in it. Like how a very smooth cake batter is easier to work with than a lumpy one. So a formal holomorphic function is like a pretend batter that is perfectly smooth and easy to work with, even if you can't taste it or use it to make a real cake.