Circular summation of theta functions in Ramanujan's Lost Notebook

Heng Huat Chan; Zhi Guo Liu; Say Tiong Ng

doi:10.1016/j.jmaa.2005.05.015

Circular summation of theta functions in Ramanujan's Lost Notebook

Heng Huat Chan, Zhi Guo Liu, Say Tiong Ng

School of Mathematical Sciences

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

20 Scopus citations

Abstract

In this paper, we prove Ramanujan's circular summation formulas previously studied by S.S. Rangachari, S.H. Son, K. Ono, S. Ahlgren and K.S. Chua using properties of elliptic and theta functions. We also derive identities similar to Ramanujan's summation formula and connect these identities to Jacobi's and Dixon's elliptic functions. At the end of the paper, we discuss the connection of our results with the recent thesis of E. Conrad.

Original language	English
Pages (from-to)	628-641
Number of pages	14
Journal	Journal of Mathematical Analysis and Applications
Volume	316
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2005.05.015
State	Published - 15 Apr 2006

Keywords

Circular summation
Dixon
Elliptic
Jacobi
Ramanujan
Theta

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abstract = "In this paper, we prove Ramanujan's circular summation formulas previously studied by S.S. Rangachari, S.H. Son, K. Ono, S. Ahlgren and K.S. Chua using properties of elliptic and theta functions. We also derive identities similar to Ramanujan's summation formula and connect these identities to Jacobi's and Dixon's elliptic functions. At the end of the paper, we discuss the connection of our results with the recent thesis of E. Conrad.",

keywords = "Circular summation, Dixon, Elliptic, Jacobi, Ramanujan, Theta",

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AU - Chan, Heng Huat

AU - Liu, Zhi Guo

AU - Ng, Say Tiong

PY - 2006/4/15

Y1 - 2006/4/15

N2 - In this paper, we prove Ramanujan's circular summation formulas previously studied by S.S. Rangachari, S.H. Son, K. Ono, S. Ahlgren and K.S. Chua using properties of elliptic and theta functions. We also derive identities similar to Ramanujan's summation formula and connect these identities to Jacobi's and Dixon's elliptic functions. At the end of the paper, we discuss the connection of our results with the recent thesis of E. Conrad.

AB - In this paper, we prove Ramanujan's circular summation formulas previously studied by S.S. Rangachari, S.H. Son, K. Ono, S. Ahlgren and K.S. Chua using properties of elliptic and theta functions. We also derive identities similar to Ramanujan's summation formula and connect these identities to Jacobi's and Dixon's elliptic functions. At the end of the paper, we discuss the connection of our results with the recent thesis of E. Conrad.

KW - Circular summation

KW - Dixon

KW - Elliptic

KW - Jacobi

KW - Ramanujan

KW - Theta

UR - https://www.scopus.com/pages/publications/29844448871

U2 - 10.1016/j.jmaa.2005.05.015

DO - 10.1016/j.jmaa.2005.05.015

M3 - 文章

AN - SCOPUS:29844448871

SN - 0022-247X

VL - 316

SP - 628

EP - 641

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

IS - 2

ER -

Circular summation of theta functions in Ramanujan's Lost Notebook

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Keywords

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