On extensions of two results due to Ramanujan

Yong Sup Kim; Arjun Kumar Rathie; Richard Bruce Paris

doi:10.3906/mat-1909-59

On extensions of two results due to Ramanujan

Yong Sup Kim^*, Arjun Kumar Rathie, Richard Bruce Paris

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

41 Downloads (Pure)

Abstract

The aim in this note is to provide a generalization of an interesting entry in Ramanujan’s notebooks that relate sums involving the derivatives of a function φ(t) evaluated at 0 and 1. The generalization obtained is derived with the help of expressions for the sum of terminating ₃F₂ hypergeometric functions of argument equal to 2, recently obtained by Kim et. al. [Two results for the terminating ₃F₂(2) with applications, Bulletin of the Korean Mathematical Society 2012; 49: 621-633]. Several special cases are given. In addition we generalize a summation formula to include integral parameter differences.

Original language	English
Pages (from-to)	348-355
Number of pages	8
Journal	Turkish Journal of Mathematics
Volume	44
Issue number	2
DOIs	https://doi.org/10.3906/mat-1909-59
Publication status	Published - 17 Mar 2020

Access to Document

10.3906/mat-1909-59Licence: CC BY

Paris_OnExtensionsOfTwoResultsDueToRamanujan_Published_2020Final published version, 162 KBLicence: CC BY

http://journals.tubitak.gov.tr/math/abstract.htm?id=26661Licence: CC BY

Cite this

@article{e66b3f78eea3402e9d45d49f8d37e136,

title = "On extensions of two results due to Ramanujan",

abstract = "The aim in this note is to provide a generalization of an interesting entry in Ramanujan{\textquoteright}s notebooks that relate sums involving the derivatives of a function φ(t) evaluated at 0 and 1. The generalization obtained is derived with the help of expressions for the sum of terminating 3F2 hypergeometric functions of argument equal to 2, recently obtained by Kim et. al. [Two results for the terminating 3F2(2) with applications, Bulletin of the Korean Mathematical Society 2012; 49: 621-633]. Several special cases are given. In addition we generalize a summation formula to include integral parameter differences.",

author = "Kim, {Yong Sup} and Rathie, {Arjun Kumar} and Paris, {Richard Bruce}",

year = "2020",

month = mar,

day = "17",

doi = "10.3906/mat-1909-59",

language = "English",

volume = "44",

pages = "348--355",

journal = "Turkish Journal of Mathematics",

issn = "1300-0098",

publisher = "TUBITAK",

number = "2",

}

TY - JOUR

T1 - On extensions of two results due to Ramanujan

AU - Kim, Yong Sup

AU - Rathie, Arjun Kumar

AU - Paris, Richard Bruce

PY - 2020/3/17

Y1 - 2020/3/17

N2 - The aim in this note is to provide a generalization of an interesting entry in Ramanujan’s notebooks that relate sums involving the derivatives of a function φ(t) evaluated at 0 and 1. The generalization obtained is derived with the help of expressions for the sum of terminating 3F2 hypergeometric functions of argument equal to 2, recently obtained by Kim et. al. [Two results for the terminating 3F2(2) with applications, Bulletin of the Korean Mathematical Society 2012; 49: 621-633]. Several special cases are given. In addition we generalize a summation formula to include integral parameter differences.

AB - The aim in this note is to provide a generalization of an interesting entry in Ramanujan’s notebooks that relate sums involving the derivatives of a function φ(t) evaluated at 0 and 1. The generalization obtained is derived with the help of expressions for the sum of terminating 3F2 hypergeometric functions of argument equal to 2, recently obtained by Kim et. al. [Two results for the terminating 3F2(2) with applications, Bulletin of the Korean Mathematical Society 2012; 49: 621-633]. Several special cases are given. In addition we generalize a summation formula to include integral parameter differences.

U2 - 10.3906/mat-1909-59

DO - 10.3906/mat-1909-59

M3 - Article

VL - 44

SP - 348

EP - 355

JO - Turkish Journal of Mathematics

JF - Turkish Journal of Mathematics

SN - 1300-0098

IS - 2

ER -