@@ Property / Symbols used @@
+Jacobi’s epsilon function
@@ Property / Symbols used: Jacobi’s epsilon function / rank @@
+Normal rank
@@ Property / Symbols used: Jacobi’s epsilon function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathcal{E}\left(\NVar{x},\NVar{k}\right)}}$ 
\JacobiEpsilonk@{\NVar{x}}{\NVar{k}}
@@ Property / Symbols used: Jacobi’s epsilon function / qualifier @@
+xml-id: C22.S16.E14.m2aqdec
@@ Property / Symbols used @@
+Jacobi’s amplitude function
@@ Property / Symbols used: Jacobi’s amplitude function / rank @@
+Normal rank
@@ Property / Symbols used: Jacobi’s amplitude function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\operatorname{am}\left(\NVar{x},\NVar{k}\right)}}$ 
\Jacobiamk@{\NVar{x}}{\NVar{k}}
@@ Property / Symbols used: Jacobi’s amplitude function / qualifier @@
+xml-id: C22.S16.E1.m2aldec
@@ Property / Symbols used @@
+Q11600
@@ Property / Symbols used: Q11600 / rank @@
+Normal rank
@@ Property / Symbols used: Q11600 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle K\left(\NVar{k}\right)}}$ 
\compellintKk@{\NVar{k}}
@@ Property / Symbols used: Q11600 / qualifier @@
+xml-id: C19.S2.E8.m1aedec
@@ Property / Symbols used @@
+Legendre’s incomplete elliptic integral of the second kind
+Normal rank
+Defining formula:  ${\displaystyle{\displaystyle E\left(\NVar{\phi},\NVar{k}\right)}}$ 
\incellintEk@{\NVar{\phi}}{\NVar{k}}
+xml-id: C19.S2.E5.m2adec
@@ Property / Symbols used @@
+Q12003
@@ Property / Symbols used: Q12003 / rank @@
+Normal rank
@@ Property / Symbols used: Q12003 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle x}}$ 
x
@@ Property / Symbols used: Q12003 / qualifier @@
+xml-id: C22.S1.XMD1.m1addec
@@ Property / Symbols used @@
+Q11984
@@ Property / Symbols used: Q11984 / rank @@
+Normal rank
@@ Property / Symbols used: Q11984 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle k}}$ 
k
@@ Property / Symbols used: Q11984 / qualifier @@
+xml-id: C22.S1.XMD4.m1abdec

DLMF:22.16.E31 (Q7151): Difference between revisions

ℰ ⁡ ( x , k ) Jacobi-Epsilon 𝑥 𝑘 {\displaystyle{\displaystyle\mathcal{E}\left(\NVar{x},\NVar{k}\right)}}

am ⁡ ( x , k ) Jacobi-elliptic-amplitude 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{am}\left(\NVar{x},\NVar{k}\right)}}

K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}

E ⁡ ( ϕ , k ) elliptic-integral-second-kind-E italic-ϕ 𝑘 {\displaystyle{\displaystyle E\left(\NVar{\phi},\NVar{k}\right)}}

x 𝑥 {\displaystyle{\displaystyle x}}

k 𝑘 {\displaystyle{\displaystyle k}}

Latest revision as of 15:37, 2 January 2020

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${\displaystyle{\displaystyle\mathcal{E}\left(\NVar{x},\NVar{k}\right)}}$

${\displaystyle{\displaystyle\operatorname{am}\left(\NVar{x},\NVar{k}\right)}}$

${\displaystyle{\displaystyle K\left(\NVar{k}\right)}}$

${\displaystyle{\displaystyle E\left(\NVar{\phi},\NVar{k}\right)}}$

${\displaystyle{\displaystyle x}}$

${\displaystyle{\displaystyle k}}$