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8 papers
Univalent Functions involving Generalized Hypergeometric Series
K. Chandrasekran, D. J. Prabhakaran
The main objective of the present article is to make interconnection between the Generalized Hyergeometric series and some subclasses of normalized analytic functions with positive…
Univalent Functions with Non-Negative Coefficients involving Clausen's Hypergeometric Function
K. Chandrasekran, G. Murugusundaramoorthy, D. J. Prabhakaran
In this work, we derived the necessary and sufficient conditions on parameters for Hypergeometric Function to be in the classes $\mathcal{M}^{\ast}(λ,…
Ramanujan's type of product of theta functions and its applications
D. J. Prabhakaran, N. Jayakumar, K. Ranjithkumar
In this paper, we initiate a generous amount of new-found general theorems for explicit evaluations of product of the theta functions using Kronecker's limit formula and…
Applications of a new P-Q modular equation of degree two
D. J. Prabhakaran, K. Ranjith kumar
At scattered places in his first notebook, Ramanujan recorded the values for 107 class invariants or irreducible monic polynomials satisfied by them. On pages 294-299 in his second…
The explicit evaluations of Ramanujan's remarkable product of theta-functions a_{m, n}
D. J. Prabhakaran, K. Ranjith kumar
On pages 338 and 339 in his first notebook, Ramanujan defined the remarkable product of theta-functions . Also he recorded eighteen explicit values depending on two param…
The Explicit Evaluations Formula for Ramanujan's Singular Moduli and Ramanujan- Selberg Continued Fraction
D. J. Prabhakaran, K. Ranjith kumar
At scattered places of his notebooks, Ramanujan recorded over 30 values of singular moduli . All those results were proved by Berndt et. al by employing Weber-Ramanujan's clas…