@@ Property / Symbols used @@
+Jacobian elliptic function
@@ Property / Symbols used: Jacobian elliptic function / rank @@
+Normal rank
@@ Property / Symbols used: Jacobian elliptic function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}$ 
\Jacobiellsnk@{\NVar{z}}{\NVar{k}}
@@ Property / Symbols used: Jacobian elliptic function / qualifier @@
+xml-id: C22.S2.E4.m2aedec
@@ Property / Symbols used @@
+Lamé polynomial
@@ Property / Symbols used: Lamé polynomial / rank @@
+Normal rank
@@ Property / Symbols used: Lamé polynomial / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathit{sdE}^{\NVar{m}}_{2\NVar{n}+2}\left(\NVar{z% },\NVar{k^{2}}\right)}}$ 
\LamepolysdE{\NVar{m}}{2\NVar{n}+2}@{\NVar{z}}{\NVar{k^{2}}}
@@ Property / Symbols used: Lamé polynomial / qualifier @@
+xml-id: C29.S12.E6.m2aadec
@@ Property / Symbols used @@
+Q12357
@@ Property / Symbols used: Q12357 / rank @@
+Normal rank
@@ Property / Symbols used: Q12357 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle m}}$ 
m
@@ Property / Symbols used: Q12357 / qualifier @@
+xml-id: C29.S1.XMD1.m1udec
@@ Property / Symbols used @@
+Q12367
@@ Property / Symbols used: Q12367 / rank @@
+Normal rank
@@ Property / Symbols used: Q12367 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle n}}$ 
n
@@ Property / Symbols used: Q12367 / qualifier @@
+xml-id: C29.S1.XMD2.m1amdec
@@ Property / Symbols used @@
+Q12359
@@ Property / Symbols used: Q12359 / rank @@
+Normal rank
@@ Property / Symbols used: Q12359 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle p}}$ 
p
@@ Property / Symbols used: Q12359 / qualifier @@
+xml-id: C29.S1.XMD3.m1acdec
@@ Property / Symbols used @@
+Q12348
@@ Property / Symbols used: Q12348 / rank @@
+Normal rank
@@ Property / Symbols used: Q12348 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle z}}$ 
z
@@ Property / Symbols used: Q12348 / qualifier @@
+xml-id: C29.S1.XMD6.m1mdec
@@ Property / Symbols used @@
+Q12350
@@ Property / Symbols used: Q12350 / rank @@
+Normal rank
@@ Property / Symbols used: Q12350 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle k}}$ 
k
@@ Property / Symbols used: Q12350 / qualifier @@
+xml-id: C29.S1.XMD8.m1ydec
@@ Property / Symbols used @@
+Q12371
@@ Property / Symbols used: Q12371 / rank @@
+Normal rank
@@ Property / Symbols used: Q12371 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle C_{2p+1}}}$ 
C_{2p+1}
@@ Property / Symbols used: Q12371 / qualifier @@
+xml-id: C29.S6.XMD7.m1hdec

DLMF:29.15.E48 (Q8793): Difference between revisions

sn ⁡ ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}

𝑠𝑑𝐸 2 ⁢ n + 2 m ⁡ ( z , k 2 ) Lame-polynomial-sdE 𝑚 2 𝑛 2 𝑧 superscript 𝑘 2 {\displaystyle{\displaystyle\mathit{sdE}^{\NVar{m}}_{2\NVar{n}+2}\left(\NVar{z% },\NVar{k^{2}}\right)}}

m 𝑚 {\displaystyle{\displaystyle m}}

n 𝑛 {\displaystyle{\displaystyle n}}

p 𝑝 {\displaystyle{\displaystyle p}}

z 𝑧 {\displaystyle{\displaystyle z}}

k 𝑘 {\displaystyle{\displaystyle k}}

C 2 ⁢ p + 1 subscript 𝐶 2 𝑝 1 {\displaystyle{\displaystyle C_{2p+1}}}

Latest revision as of 01:38, 2 January 2020

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${\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}$

${\displaystyle{\displaystyle\mathit{sdE}^{\NVar{m}}_{2\NVar{n}+2}\left(\NVar{z% },\NVar{k^{2}}\right)}}$

${\displaystyle{\displaystyle m}}$

${\displaystyle{\displaystyle n}}$

${\displaystyle{\displaystyle p}}$

${\displaystyle{\displaystyle z}}$

${\displaystyle{\displaystyle k}}$

${\displaystyle{\displaystyle C_{2p+1}}}$