DLMF:22.16.E2 (Q7121): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Jacobi’s amplitude function / rank
 
Normal rank
Property / Symbols used: Jacobi’s amplitude function / qualifier
 
Defining formula:

am ( x , k ) Jacobi-elliptic-amplitude 𝑥 𝑘 {\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.m2aadec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q11600 / rank
 
Normal rank
Property / Symbols used: Q11600 / qualifier
 
Defining formula:

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

\compellintKk@{\NVar{k}}
Property / Symbols used: Q11600 / qualifier
 
xml-id: C19.S2.E8.m1adec
Property / Symbols used
 
Property / Symbols used: Q12003 / rank
 
Normal rank
Property / Symbols used: Q12003 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12003 / qualifier
 
xml-id: C22.S1.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q11984 / rank
 
Normal rank
Property / Symbols used: Q11984 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11984 / qualifier
 
xml-id: C22.S1.XMD4.m1adec

Latest revision as of 15:30, 2 January 2020

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DLMF:22.16.E2
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    Statements

    am ( x + 2 K , k ) = am ( x , k ) + π . Jacobi-elliptic-amplitude 𝑥 2 𝐾 𝑘 Jacobi-elliptic-amplitude 𝑥 𝑘 𝜋 {\displaystyle{\displaystyle\operatorname{am}\left(x+2K,k\right)=\operatorname% {am}\left(x,k\right)+\pi.}}
    0 references
    DLMF:22.16.E2
    0 references
    am ( x , k ) Jacobi-elliptic-amplitude 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{am}\left(\NVar{x},\NVar{k}\right)}}
    C22.S16.E1.m2aadec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
    0 references
    K ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    C19.S2.E8.m1adec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C22.S1.XMD1.m1adec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C22.S1.XMD4.m1adec
    0 references