# Some extensions for Ramanujan's circular summation formula

## TL;DR

This paper extends Ramanujan's circular summation formula to include mixed products of two Jacobi theta functions and derives new identities, broadening the understanding of theta function relationships.

## Contribution

It introduces novel extensions of Ramanujan's formula involving mixed theta function products and presents new identities of Jacobi's theta functions.

## Key findings

- Extended Ramanujan's circular summation formula with mixed products
- Derived new identities of Jacobi's theta functions
- Enhanced understanding of theta function relationships

## Abstract

In this paper, we give some extensions for Ramanujan's circular summation formula with the mixed products of two Jacobi's theta functions. As some applications, we also obtain many interesting identities of Jacobi's theta functions.