Ramanujan’s Circular Summation And Ramanujan’s Lost Notebook

Ramanujan is a great India mathematician,he has a strong intuitive insight in mathematics,and has made an important contribution in the field of integer partition, elliptic functions,hypergeometric functions and series.He left three notebooks, two of which are Ramanujan’s notebooks and the last one is Ramanujan’s lost notebook, we usually use theta function structure rational characteristics of elliptic function to research ?1and ?2problems. This paper is divided into four main parts, in the first part,I introduces the meaning and backdrop of the task;the second part, I introduces the Ramanujan’three notebooks, I describes in detail the discovery, collating and publishing of the Ramanujan lost notebooks;the third part, on the basis of the elliptic function and theta theory,I mainly discusses the circulation formula、 the virtual transformation form and the staggered circulation formula of the function ?1and ?1;the fourth part,I mainly discusses the application of the function ?1and ?1.