Geodesic
On asymptotics of elliptic sine
Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 2, pp. 169-180

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The article offers a simple way of the finding of the elliptic sine $z={\rm sn}(u;k)$ asymptotics by powers of $k^2-1$. In the literary sources only the first two members decomposition discharged. The proposed method allows to find the subsequent terms of the expansion. The disadvantage is the large amount of calculations. The main result is that the asymptotic expansion is not uniform by $u$ when $k\to 1$. The assessment of the remainder term of the decomposition is received also.
Keywords: elliptic sine, asymptotic expansion, hyperbolic functions. 
@article{CHFMJ_2017_2_2_a2,
     author = {A. V. Krasilnikov},
     title = {On asymptotics of elliptic sine},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {169--180},
     publisher = {mathdoc},
     volume = {2},
     number = {2},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_2_a2/}
}
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A. V. Krasilnikov. On asymptotics of elliptic sine. Čelâbinskij fiziko-matematičeskij žurnal, Tome 2 (2017) no. 2, pp. 169-180. http://geodesic.mathdoc.fr/item/CHFMJ_2017_2_2_a2/