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 $$\int _0^x \text {d}t/\sqrt{1-t^6}$$ ∫ 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.

Applications of a duality between generalized trigonometric and hyperbolic functions II

“…[4] 6 (6/5, 2) Takeuchi [13] (2, 6) Shinohara [11] (6/5, 6) Takeuchi [13] q (2q/(2 + q), q/2) (2q/(2 + q), q) (q/2, q) 2 (1, 1) Napier (1, 2) V. Riccati (1, 2) V. Riccati 3 (6/5, 3/2) Theorem 4.4…”