Milne, Steven C. (2000). "Hankel Determinants of Eisenstein Series". arXiv:math/0009130v3. The paper uses a non-equivalent definition of , but this has been accounted for in this article.
books.google.com
Gareth A. Jones and David Singerman. (1987) Complex functions: an algebraic and geometric viewpoint. Cambridge UP. [1]
The equality holds if the arithmetic–geometric mean of complex numbers (such that ) is defined as follows: Let , , , where the signs are chosen such that for all . If , the sign is chosen such that . Then . When are positive real (with ), this definition coincides with the usual definition of the arithmetic–geometric mean for positive real numbers. See The Arithmetic-Geometric Mean of Gauss by David A. Cox.
Girondo, Ernesto; González-Diez, Gabino (2012), Introduction to compact Riemann surfaces and dessins d'enfants, London Mathematical Society Student Texts, vol. 79, Cambridge: Cambridge University Press, p. 267, ISBN978-0-521-74022-7, Zbl1253.30001