A Note on Somos's Identities of Level 6.

Authors :: Radha, D. Anu
Kumar, B. R. Srivatsa
N. V., Sayinath Udupa
Source :: IAENG International Journal of Applied Mathematics. Jun2022, Vol. 52 Issue 2, p386-390. 5p.
Publication Year :: 2022
Abstract: Michael Somos conjectured thousands of theta-functions of various levels with the help of computer and not provided the proof. These theta-functions highly matches Ramanujan's recordings. The objective of our work in this paper is to prove two theta-functions of level 6 conjectured by Somos and to give an alternate proof of the identities proved by B. R. Srivatsa Kumar and G. Sharath. Further, as an application of this, we offer colored partition identities for the same. [ABSTRACT FROM AUTHOR]