A form of verb

Hey Guys I could not get the usage of the word write in the sentence given below, I mean, it is not in form of gerund or infinity. thanks for your help.

“I need your photographic memory and your passion for social upheaval to help me write the book about the Upper East Side.”

It’s an assumed form of the infinitive.
The complete sentence would be
‘… to help me to write the book’
but the second ‘to’ is dropped and assumed, avoiding the close repetition of the word.

Thank you very much.