English

Legendre-type relations for generalized complete elliptic integrals

Classical Analysis and ODEs 2020-03-25 v2

Abstract

Legendre's relation for the complete elliptic integrals of the first and second kinds is generalized. The proof depends on an application of the generalized trigonometric functions and is alternative to the proof for Elliott's identity.

Keywords

Cite

@article{arxiv.1606.05115,
  title  = {Legendre-type relations for generalized complete elliptic integrals},
  author = {Shingo Takeuchi},
  journal= {arXiv preprint arXiv:1606.05115},
  year   = {2020}
}

Comments

10 pages

R2 v1 2026-06-22T14:26:48.637Z