Gold 26

Jacobi elliptic functions

Gold ID

26

Link

https://sigir21.wmflabs.org/wiki/Jacobi_elliptic_functions#math.76.155

Formula

${\frac {\mathrm {d} }{\mathrm {d} z}}\operatorname {dn} (z)=-k^{2}\operatorname {sn} (z)\operatorname {cn} (z)$

TeX Source

\frac{\mathrm{d}}{\mathrm{d}z} \operatorname{dn}(z) = - k^2 \operatorname{sn}(z) \operatorname{cn}(z)

Translation Results
Semantic LaTeX	Mathematica Translation	Maple Translations

Semantic LaTeX

Translation

\deriv [1]{ }{z} \Jacobielldnk@@{(z)}{k} = - k^2 \Jacobiellsnk@@{(z)}{k} \Jacobiellcnk@@{(z)}{k}

Expected (Gold Entry)

\deriv [1]{ }{z} \Jacobielldnk@@{(z)}{k} = - k^2 \Jacobiellsnk@@{(z)}{k} \Jacobiellcnk@@{(z)}{k}

Mathematica

Translation

D[JacobiDN[z, (k)^2], {z, 1}] == - (k)^(2)* JacobiSN[z, (k)^2]*JacobiCN[z, (k)^2]

Expected (Gold Entry)

D[JacobiDN[z, (k)^2], {z, 1}] == - (k)^(2)* JacobiSN[z, (k)^2]*JacobiCN[z, (k)^2]

Maple

Translation

diff(JacobiDN(z, k), [z$(1)]) = - (k)^(2)* JacobiSN(z, k)*JacobiCN(z, k)

Expected (Gold Entry)

diff(JacobiDN(z, k), [z$\$$(1)]) = - (k)^(2)* JacobiSN(z, k)*JacobiCN(z, k)