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Difference between revisions of "Tangent amplitude"

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The ratio of the two basic [[Jacobi elliptic functions|Jacobi elliptic functions]]:
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The ratio of the two basic [[Jacobi elliptic functions]]:
 
 
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/t/t092/t092100/t0921001.png" /></td> </tr></table>
 
 
 
 
 
 
 
====Comments====
 
  
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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,   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>
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<table>
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<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>
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<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>
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<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>
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</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
This article was adapted from an original article by E.D. Solomentsev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article