Mellin inversion theorem

Mellin inversion theorem is like doing a magic trick with numbers. You see, when you have a math problem, sometimes it's easier to change it into another problem so you can solve it better. Mellin inversion theorem helps you do that.

Let's imagine you have a big pizza, and you want to know how much of it is cheese. You could just count the cheese pieces, but what if the cheese is all melted together and mixed with the sauce? It's harder to count that way, right? So, you might think of another way to figure it out.

That's what Mellin inversion theorem does. It changes the math problem into another problem that's easier to solve, and then changes it back when you're done.

It works like this: first, you take your original math problem and change it into something called the Mellin transform. Think of transforming a toy car into a toy robot, just by rearranging the parts. Then, you use some special math rules to solve the transformed problem. This is like taking apart the toy robot, figuring out how it works, and then putting it back together as a car.

Finally, you use the Mellin inversion theorem to change the solution back into the answer to your original problem. This is like turning the toy car back into a robot.

So, to sum it up: Mellin inversion theorem is a magic math trick that helps you solve problems by turning them into something easier, solving that thing, and then turning the solution back into the answer to the original problem.