English

Some double-angle formulas related to a generalized lemniscate function

Classical Analysis and ODEs 2021-12-28 v1 Analysis of PDEs

Abstract

In this paper we will establish some double-angle formulas related to the inverse function of 0xdt/1t6\int_0^x dt/\sqrt{1-t^6}. This function appears in Ramanujan's Notebooks and is regarded as a generalized version of the lemniscate function.

Keywords

Cite

@article{arxiv.1912.11483,
  title  = {Some double-angle formulas related to a generalized lemniscate function},
  author = {Shingo Takeuchi},
  journal= {arXiv preprint arXiv:1912.11483},
  year   = {2021}
}

Comments

9 pages. arXiv admin note: text overlap with arXiv:1904.09880

R2 v1 2026-06-23T12:55:58.923Z