Some double-angle formulas related to a generalized lemniscate function

In this paper, we will establish some double-angle formulas related to the inverse function of ∫ 0 x d t / 1 - t 6 . This function appears in Ramanujan’s Notebooks and is regarded as a generalized version of the lemniscate function.

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Bibliographic Details
Published in:The Ramanujan journal 2021-11, Vol.56 (2), p.753-761
Main Author: Takeuchi, Shingo
Format: Article
Language:English
Subjects:
Combinatorics
Field Theory and Polynomials
Fourier Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Number Theory
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Description
Summary:In this paper, we will establish some double-angle formulas related to the inverse function of ∫ 0 x d t / 1 - t 6 . This function appears in Ramanujan’s Notebooks and is regarded as a generalized version of the lemniscate function.
ISSN:1382-4090
1572-9303
DOI:10.1007/s11139-021-00395-x