|
|||||
|
|
The explicit formulas and evaluations of Ramanujan's theta-function ψ |
|
| Authors: | Jinhee Yi Yang Lee |
| Affiliation: | a Department of Mathematics, Korea Science Academy, Republic of Korea b Department of Mathematics, Pusan National University, Republic of Korea c Department of Mathematics Education, Busan National University of Education, Republic of Korea |
| Abstract: | We define two quotients of theta-function ψ depending on two positive real parameters. We then show how they are connected with two parameters of Dedekind eta-function, theta-function φ, and the Ramanujan-Weber class invariants. Explicit formulas for determining values of the theta-function ψ are derived, and several examples will be given. In addition, we give some applications of these parameters for the famous Rogers-Ramanujan continued fraction R(q), Ramanujan's cubic continued fraction G(q), and the modular j-invariant. |
| Keywords: | Theta-functions Classical hypergeometric functions Modular equations Continued fractions |
| 本文献已被 ScienceDirect 等数据库收录！ | |