Contributions to the Theory of Special Functions and Number Theory

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 new general theorems for the explicit evaluations of Ramanujan's remarkable product of theta function and their new explicit assessment.He has also established several new P - Q eta-function identities which were obtained, leading to several new modular relations for the Ramanujan-Göllnitz-Gordon continued fraction.He has obtained a continued fraction of order 12 and evaluated several new identities analogous to the Rogers-Ramanujan continued fraction and Ramanujan's cubic continued fraction.He has derived some new modular equations of degree 5 for the ratios of Ramanujan's theta function and new modular relations for Ramanujan's parameters related to Rogers-Ramanujan's continued fraction were also established along with their explicit evaluations.

Autorentext
Dr. Dharmendra B. N. works as an Associate Professor in the Department of Mathematics, Government College for Women, Kolar. He has 18 years of teaching experience and published over 50 research articles in reputed National and International Journals. His area of interest is the Theory of numbers, modular equations and their applications.