Tangent amplitude

The ratio of the two basic Jacobi elliptic functions:

$$\operatorname{sc}u=\tan\operatorname{am}u=\frac{\operatorname{sn}u}{\operatorname{cn}u}.$$

References

[a1]	A. Hurwitz, R. Courant, "Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen" , 1 , Springer (1964)
[a2]	E.T. Whittaker, G.N. Watson, "A course of modern analysis" , Cambridge Univ. Press (1952) pp. Chapt. 6
[a3]	J. Tannéry, J. Molk, "Eléments de la théorie des fonctions elliptiques" , 1–2 , Chelsea, reprint (1972)