Minor Functions
Reversing the order of the two letters of the function name results in the reciprocals of the three functions above:
Similarly, the ratios of the three primary functions correspond to the first letter of the numerator followed by the first letter of the denominator:
More compactly, we have
where each of p, q, and r is any of the letters s, c, d, n, with the understanding that ss = cc = dd = nn = 1.
(This notation is due to Gudermann and Glaisher and is not Jacobi's original notation.)
Read more about this topic: Jacobi Elliptic Functions
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