Abstract
In the case of trigonometric functions, we can rewrite the familiar identity
as
where y(z) = sinz. We can retrieve the inverse function of sine by formally integrating
so that
The period of the sine function can also be retrieved from
However, we should be cautious about this reasoning since sin−1 z is a multi-valued function and the integral may depend on the path taken from 0 to z. With this understanding, let us try to treat the inverse of the elliptic function \(\wp (z)\) in a similar way. Indeed, we have
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Bibliography
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Murty, M.R., Rath, P. (2014). Transcendental Values of Some Elliptic Integrals. In: Transcendental Numbers. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0832-5_13
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DOI: https://doi.org/10.1007/978-1-4939-0832-5_13
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