@@ Property / Symbols used @@
+Q11661
@@ Property / Symbols used: Q11661 / rank @@
+Normal rank
@@ Property / Symbols used: Q11661 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle U_{\NVar{n}}\left(\NVar{x}\right)}}$ 
\ChebyshevpolyU{\NVar{n}}@{\NVar{x}}
@@ Property / Symbols used: Q11661 / qualifier @@
+xml-id: C18.S3.T1.t1.r5.m2adec
@@ Property / Symbols used @@
+Jacobian elliptic function
@@ Property / Symbols used: Jacobian elliptic function / rank @@
+Normal rank
@@ Property / Symbols used: Jacobian elliptic function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}$ 
\Jacobiellcnk@{\NVar{z}}{\NVar{k}}
@@ Property / Symbols used: Jacobian elliptic function / qualifier @@
+xml-id: C22.S2.E5.m2adec
@@ 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.m2abdec
@@ Property / Symbols used @@
+Lamé polynomial
@@ Property / Symbols used: Lamé polynomial / rank @@
+Normal rank
@@ Property / Symbols used: Lamé polynomial / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathit{cE}^{\NVar{m}}_{2\NVar{n}+1}\left(\NVar{z}% ,\NVar{k^{2}}\right)}}$ 
\LamepolycE{\NVar{m}}{2\NVar{n}+1}@{\NVar{z}}{\NVar{k^{2}}}
@@ Property / Symbols used: Lamé polynomial / qualifier @@
+xml-id: C29.S12.E3.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.m1rdec
@@ 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.m1ajdec
@@ 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.m1zdec
@@ 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.m1jdec
@@ 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.m1vdec
@@ Property / Symbols used @@
+Q12372
@@ Property / Symbols used: Q12372 / rank @@
+Normal rank
@@ Property / Symbols used: Q12372 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle B_{2p+1}}}$ 
B_{2p+1}
@@ Property / Symbols used: Q12372 / qualifier @@
+xml-id: C29.S6.XMD9.m1dec

DLMF:29.15.E45 (Q8790): Difference between revisions

U n ⁡ ( x ) Chebyshev-polynomial-second-kind-U 𝑛 𝑥 {\displaystyle{\displaystyle U_{\NVar{n}}\left(\NVar{x}\right)}}

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

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

𝑐𝐸 2 ⁢ n + 1 m ⁡ ( z , k 2 ) Lame-polynomial-cE 𝑚 2 𝑛 1 𝑧 superscript 𝑘 2 {\displaystyle{\displaystyle\mathit{cE}^{\NVar{m}}_{2\NVar{n}+1}\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}}

B 2 ⁢ p + 1 subscript 𝐵 2 𝑝 1 {\displaystyle{\displaystyle B_{2p+1}}}

Latest revision as of 01:37, 2 January 2020

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${\displaystyle{\displaystyle U_{\NVar{n}}\left(\NVar{x}\right)}}$

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

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

${\displaystyle{\displaystyle\mathit{cE}^{\NVar{m}}_{2\NVar{n}+1}\left(\NVar{z}% ,\NVar{k^{2}}\right)}}$

${\displaystyle{\displaystyle m}}$

${\displaystyle{\displaystyle n}}$

${\displaystyle{\displaystyle p}}$

${\displaystyle{\displaystyle z}}$

${\displaystyle{\displaystyle k}}$

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