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On Some Modular Equations in the Spirit of Ramanujan
Srivatsa Kumar, Belakavadi Radhakrishna Department of Mathematics 2016 Kyungpook mathematical journal Vol.56 No.3
In this paper, we establish some new P-Q type modular equations, by using the modular equations given by Srinivasa Ramanujan.
Kumar, Belakavadi Radhakrishna Srivatsa,Vidya, Harekala Chandrashekara Department of Mathematics 2018 Kyungpook mathematical journal Vol.58 No.2
In the present paper, we establish relationship between continued fraction U(-q) of order 12 and Ramanujan's cubic continued fraction G(-q) and $G(q^n)$ for n = 1, 2, 3, 5 and 7. Also we evaluate U(q) and U(-q) by using two parameters for Ramanujan's theta-functions and their explicit values.
A note on modular equations of signature 2 and their evaluations
Belakavadi Radhakrishna Srivatsa Kumar,Arjun Kumar Rathie,Nagara Vinayaka Udupa Sayinath,SHRUTHI 대한수학회 2022 대한수학회논문집 Vol.37 No.1
In his notebooks, Srinivasa Ramanujan recorded several modular equations that are useful in the computation of class invariants, continued fractions and the values of theta functions. In this paper, we prove some new modular equations of signature 2 by well-known and useful theta function identities of composite degrees. Further, as an application of this, we evaluate theta function identities.
SOME THETA-FUNCTION IDENTITIES OF LEVEL SIX AND ITS APPLICATIONS TO PARTITIONS
B. R. SRIVATSA KUMAR,ANUSHA KUMARI 장전수학회 2018 Advanced Studies in Contemporary Mathematics Vol.28 No.1
In this paper, we prove theta-function identities dis- covered by Somos which highly resembles Ramanujan's recordings and also establish partition identities for them.
B. R. SRIVATSA KUMAR,임동규,Arjun K. Rathie 한국수학교육학회 2023 純粹 및 應用數學 Vol.30 No.2
The aim of this note is to provide two new and interesting closed-form evaluations of the generalized hypergeometric function $_5F_4$ with argument $1/256$. This is achieved by means of separating a generalized hypergeometric function into even and odd components together with the use of two known sums (one each) involving reciprocals of binomial coefficients obtained earlier by Trif and Sprugnoli. In the end, the results are written in terms of two interesting combinatorial identities
Arithmetic identities of Ramanujan's general partition function for modulo 17
SHRUTHI,B. R. SRIVATSA KUMAR 장전수학회 2019 Proceedings of the Jangjeon mathematical society Vol.22 No.4
In this paper, we prove four innite families of congruences modulo 17 for the general partition function pr(n) for negative values of r. Our emphasis throughout this paper is to exhibit the use of q- identities to generate congruences for the general partition function.