Some double-angle formulas related to a generalized lemniscate function

Shingo Takeuchi

doi:10.1007/s11139-021-00395-x

Some double-angle formulas related to a generalized lemniscate function

Shingo Takeuchi

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

2 Citations (Scopus)

Abstract

In this paper, we will establish some double-angle formulas related to the inverse function of ∫0xdt/1-t6. This function appears in Ramanujan’s Notebooks and is regarded as a generalized version of the lemniscate function.

Original language	English
Pages (from-to)	753-761
Number of pages	9
Journal	Ramanujan Journal
Volume	56
Issue number	2
DOIs	https://doi.org/10.1007/s11139-021-00395-x
Publication status	Published - 2021 Nov

Keywords

Double-angle formulas
Generalized trigonometric functions
Jacobian elliptic functions
Lemniscate function
p-Laplacian

ASJC Scopus subject areas

Algebra and Number Theory

Access to Document

10.1007/s11139-021-00395-x

Cite this

@article{e157f05931d64919848aea4b8819ee17,

title = "Some double-angle formulas related to a generalized lemniscate function",

abstract = "In this paper, we will establish some double-angle formulas related to the inverse function of ∫0xdt/1-t6. This function appears in Ramanujan{\textquoteright}s Notebooks and is regarded as a generalized version of the lemniscate function.",

keywords = "Double-angle formulas, Generalized trigonometric functions, Jacobian elliptic functions, Lemniscate function, p-Laplacian",

author = "Shingo Takeuchi",

note = "Funding Information: The work was supported by JSPS KAKENHI Grant Number 17K05336. Publisher Copyright: {\textcopyright} 2021, The Author(s).",

year = "2021",

month = nov,

doi = "10.1007/s11139-021-00395-x",

language = "English",

volume = "56",

pages = "753--761",

journal = "Ramanujan Journal",

issn = "1382-4090",

publisher = "Springer Netherlands",

number = "2",

}

TY - JOUR

T1 - Some double-angle formulas related to a generalized lemniscate function

AU - Takeuchi, Shingo

PY - 2021/11

Y1 - 2021/11

N2 - In this paper, we will establish some double-angle formulas related to the inverse function of ∫0xdt/1-t6. This function appears in Ramanujan’s Notebooks and is regarded as a generalized version of the lemniscate function.

AB - In this paper, we will establish some double-angle formulas related to the inverse function of ∫0xdt/1-t6. This function appears in Ramanujan’s Notebooks and is regarded as a generalized version of the lemniscate function.

KW - Double-angle formulas

KW - Generalized trigonometric functions

KW - Jacobian elliptic functions

KW - Lemniscate function

KW - p-Laplacian

UR - http://www.scopus.com/inward/record.url?scp=85104406064&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85104406064&partnerID=8YFLogxK

U2 - 10.1007/s11139-021-00395-x

DO - 10.1007/s11139-021-00395-x

M3 - Article

AN - SCOPUS:85104406064

SN - 1382-4090

VL - 56

SP - 753

EP - 761

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 2

ER -

Some double-angle formulas related to a generalized lemniscate function

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this