DLMF:29.15.E45 (Q9482): Difference between revisions

@@ Property / Symbols used @@
+Chebyshev polynomial of the second kind
@@ Property / Symbols used: Chebyshev polynomial of the second kind / rank @@
+Normal rank
@@ Property / Symbols used: Chebyshev polynomial of the second kind / qualifier @@
+DLMF defining formula:  ${\displaystyle{\displaystyle U_{\NVar{n}}\left(\NVar{x}\right)}}$ 
\ChebyshevpolyU{\NVar{n}}@{\NVar{x}}
@@ Property / Symbols used: Chebyshev polynomial of the second kind / 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 @@
+DLMF 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 @@
+DLMF 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 @@
+DLMF 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 @@
+nonnegative integer
@@ Property / Symbols used: nonnegative integer / rank @@
+Normal rank
@@ Property / Symbols used: nonnegative integer / qualifier @@
+DLMF defining formula:  ${\displaystyle{\displaystyle m}}$ 
m
@@ Property / Symbols used: nonnegative integer / qualifier @@
+xml-id: C29.S1.XMD1.m1rdec
@@ Property / Symbols used @@
+nonnegative integer
@@ Property / Symbols used: nonnegative integer / rank @@
+Normal rank
@@ Property / Symbols used: nonnegative integer / qualifier @@
+DLMF defining formula:  ${\displaystyle{\displaystyle n}}$ 
n
@@ Property / Symbols used: nonnegative integer / qualifier @@
+xml-id: C29.S1.XMD2.m1ajdec
@@ Property / Symbols used @@
+nonnegative integer
@@ Property / Symbols used: nonnegative integer / rank @@
+Normal rank
@@ Property / Symbols used: nonnegative integer / qualifier @@
+DLMF defining formula:  ${\displaystyle{\displaystyle p}}$ 
p
@@ Property / Symbols used: nonnegative integer / qualifier @@
+xml-id: C29.S1.XMD3.m1zdec
@@ Property / Symbols used @@
+complex variable
@@ Property / Symbols used: complex variable / rank @@
+Normal rank
@@ Property / Symbols used: complex variable / qualifier @@
+DLMF defining formula:  ${\displaystyle{\displaystyle z}}$ 
z
@@ Property / Symbols used: complex variable / qualifier @@
+xml-id: C29.S1.XMD6.m1jdec
@@ Property / Symbols used @@
+real parameter
@@ Property / Symbols used: real parameter / rank @@
+Normal rank
@@ Property / Symbols used: real parameter / qualifier @@
+DLMF defining formula:  ${\displaystyle{\displaystyle k}}$ 
k
@@ Property / Symbols used: real parameter / qualifier @@
+xml-id: C29.S1.XMD8.m1vdec
@@ Property / Symbols used @@
+coefficents
@@ Property / Symbols used: coefficents / rank @@
+Normal rank
@@ Property / Symbols used: coefficents / qualifier @@
+DLMF defining formula:  ${\displaystyle{\displaystyle B_{2p+1}}}$ 
B_{2p+1}
@@ Property / Symbols used: coefficents / qualifier @@
+xml-id: C29.S6.XMD9.m1dec
@@ Property / instance of @@
+Digital Library of Mathematical Functions Formula
+Normal rank
@@ Property / MaRDI profile type @@
+MaRDI formula profile
@@ Property / MaRDI profile type: MaRDI formula profile / rank @@
+Normal rank
@@ links / mardi / name / links / mardi / name @@
+Formula:9482

DLMF:29.15.E45 (Q9482): 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 09:07, 3 March 2024

Statements

Identifiers

Sitelinks

Mathematics(1 entry)

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

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

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

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

${\displaystyle{\displaystyle m}}$

${\displaystyle{\displaystyle n}}$

${\displaystyle{\displaystyle p}}$

${\displaystyle{\displaystyle z}}$

${\displaystyle{\displaystyle k}}$

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