SOME STUDIES ON THETA FUNCTIONS AND THEIR RELATED IDENTITIES

The author has given a brief introduction of an all-time great Mathematician Srinivasa Ramanujan, the man who reshaped twentieth-century mathematics with his various contributions in several mathematical domains, including Mathematical analysis, Infinite series, Continued fractions, Number theory and Game theory.He has established several interesting and new explicit evaluations for newly defined parameters by using Ramanujan Weber class invariants, modular equations and mixed-modular equations.He has established several new explicit evaluations of Ramanujan's remarkable product of theta-function.He has established some new general theorems for explicit evaluations of the product of theta-function.He has derived several general formulas for explicit evaluations of Ramanujan's cubic continued fractions, reciprocity theorems, two formulas connecting V(q) and V(q3) and also established some explicit evaluations using the values of the remarkable product of theta-function.He has obtained a modular transformation formula for the theta-function.