Abstract
Chapters 16–21 in his second notebook [22] contain much of Ramanujan’s prodigious outpouring of discoveries about theta-functions and modular equations. However, the unorganized pages in the second and third notebooks also embrace a large amount of Ramanujan’s findings on these topics. In this chapter, we shall discuss most of this material. In Chapter 33 (Part V [9]), we relate Ramanujan’s fascinating theories of elliptic functions and modular equations with alternative bases. Chapter 26 contains Ramanujan’s theorems on inversion formulas for the lemniscate and allied integrals. Some material that normally would be placed in the present chapter is connected with continued fractions and so has been put in Chapter 32 (Part V [9]) on continued fractions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
