Certain Summation Formulas Due to Ramanujan and Their Generalizations

Arjun, K Rathie; Malani, Shaloo; Mathur, Rachana; Choi, Jeong‐Yeol

doi:10.4134/bkms.2005.42.3.469

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Cited by 3 publications

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“…which is seen to be the special case of generalized Kummer's theorem (6). Therefore it can easily be evaluated by (6) and we get the right -hand side of the Theorem 2.2.…”

Section: Main Summationmentioning

confidence: 94%

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Another Generalization of a Ramanujan Summation

Lee¹,

Lee²,

Kim³

2013

Honam Mathematical Journal

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Abstract. The aim of this research paper is to provide certain generalizations of two well-known summations due to Ramanujan. The results are derived with the help of the generalized Dixon's theorem on the sum of 3F2 and the generalized Kummer's theorem for 2F1 obtained earlier by Lavoie et al. [3,5]. As their special cases, we have obtained fifteen interesting summations which are closely related to Ramanujan's summation.

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“…which is seen to be the special case of generalized Kummer's theorem (6). Therefore it can easily be evaluated by (6) and we get the right -hand side of the Theorem 2.2.…”

Section: Main Summationmentioning

confidence: 94%

“…For i = 0, we have Remark 3.1. For another summations due to Ramanujan and their generalizations, the interested reader can consult [5,6]. If we take z = …”

Section: 5mentioning

confidence: 99%