TY - JOUR
T1 - Modular identities for some special cases of Ramanujan’s general continued fraction
AU - Bhat, Shruthi C.
AU - Srivastava, H. M.
AU - Srivatsa Kumar, B. R.
N1 - Publisher Copyright:
© The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2025.
PY - 2025/4
Y1 - 2025/4
N2 - In this article, we first introduce the continued fractions K(q), L(q) and M(q), which are based on the Ramanujan-Selberg continued fraction C(q). We then obtain several modular identities which connect K(q) with K(-q) and K(qi)(i=2,3,5,7), L(q) with L(-q) and L(qj)(j=2,3), M(q) with M(-q) and M(qj)(j=2,3), and C(q) with C(-q). We also provide some algebraic results associated with K(q) and L(q). In addition, as an application of our results, we deduce a few fascinating colored partitions which also validate the results.
AB - In this article, we first introduce the continued fractions K(q), L(q) and M(q), which are based on the Ramanujan-Selberg continued fraction C(q). We then obtain several modular identities which connect K(q) with K(-q) and K(qi)(i=2,3,5,7), L(q) with L(-q) and L(qj)(j=2,3), M(q) with M(-q) and M(qj)(j=2,3), and C(q) with C(-q). We also provide some algebraic results associated with K(q) and L(q). In addition, as an application of our results, we deduce a few fascinating colored partitions which also validate the results.
UR - https://www.scopus.com/pages/publications/85217541660
UR - https://www.scopus.com/inward/citedby.url?scp=85217541660&partnerID=8YFLogxK
U2 - 10.1007/s13398-025-01706-3
DO - 10.1007/s13398-025-01706-3
M3 - Article
AN - SCOPUS:85217541660
SN - 1578-7303
VL - 119
JO - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
JF - Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas
IS - 2
M1 - 39
ER -