Who created the rasengan ?

  What is a rasengan?

A rasengan is a A-RANKED ninjutsu which involves the gathering and spinning of chakra in different directions  (spherical in shape) The rasengan is an incomplete jutsu because for years, nature chakra couldn't be added to the rasengan but naruto was able to do it when he was mastering his nature affinity (wind).
A complete rasengan is a rasengan which is composed of ones chakra and nature affinity . While an incomplete rasengan is a rasengan which is only composed of only the user chakra.

Theory of the rasengan.

The rasengan was created by minato , the 4th hokage . He came up,with the idea of creating somethings similar to the tail beast bomb after observing it. It took it 3 years to develop the jutsu.

Many are confused because they saw the similar rasengan done by Ashura . Note , Ashura performed something similar to the rasengan called amenomihashira.

Ashura didn't follow the principles of the rasengan which is ; the principle of  gathering chakra and rotating it, adding nature release (at least one) and containment. 
After some few years he didn't require hand seal because he had mastered it . During his battle with Indra, his brother , Indra used the Amaterasu to counter ashura's amenomihashira but it didn't burn and we all know that Amaterasu burns anything it comes in contact with. But in this case the mini balls of chakra was released ,note naruto also creates mini balls outside his rasengan so in this case
amenomihashira is a form of rasengan.





Don't forget naruto has created different varieties of the rasengan such as giant rasengan,massive Rasengan,rasenshuriken

But we can't say naruto is the creator of the rasengan just because he created different varieties of the rasengan even boruto created his variety of the rasengan which he calls the vanishing rasengan

Some Naruto forms of rasengan.

Naruto  was able to master the rasengan , and with time naruto created several types of rasengan that aids  him in battle such as planetary rasengan 

This rasengan was created by Naruto by simply creating mini rasengan ball on top his main rasengan.

Another  type is the massive

 For Naruto to perform this Justu he garters a lot of chakra and sometimes infuse his sage chakra in it to make it bigger and stronger.

Boruto vanishing rasengan 

   

Boruto failure to perform the rasengan made him to create this jutsu unknowingly, he infuse too much lightning nature chakra into his rasengan in order to make it big but unknowingly he creates a new jutsu.

Minato and Naruto super rasengan.

Minato was working on the super rasengan which involves two similar chakra to resonate with each other to form the super rasengan , though it was shown on in 

"Naruto shippuden the movie : The lost tower".