Difference between revisions of "Tangent amplitude"
From Encyclopedia of Mathematics
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| − | The ratio of the two basic [[ | + | The ratio of the two basic [[Jacobi elliptic functions]]: |
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| + | $$\operatorname{sc}u=\tan\operatorname{am}u=\frac{\operatorname{sn}u}{\operatorname{cn}u}.$$ | ||
====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> A. Hurwitz, | + | <table> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> A. Hurwitz, R. Courant, "Vorlesungen über allgemeine Funktionentheorie und elliptische Funktionen" , '''1''' , Springer (1964)</TD></TR> | ||
| + | <TR><TD valign="top">[a2]</TD> <TD valign="top"> E.T. Whittaker, G.N. Watson, "A course of modern analysis" , Cambridge Univ. Press (1952) pp. Chapt. 6</TD></TR> | ||
| + | <TR><TD valign="top">[a3]</TD> <TD valign="top"> J. Tannéry, J. Molk, "Eléments de la théorie des fonctions elliptiques" , '''1–2''' , Chelsea, reprint (1972)</TD></TR> | ||
| + | </table> | ||
Latest revision as of 06:06, 23 April 2023
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) |
How to Cite This Entry:
Tangent amplitude. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Tangent_amplitude&oldid=12670
Tangent amplitude. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Tangent_amplitude&oldid=12670
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article