DLMF:22.15.E14 (Q7109): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1acdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3acdec
Property / Symbols used
 
Property / Symbols used: Q12009 / rank
 
Normal rank
Property / Symbols used: Q12009 / qualifier
 
Defining formula:

arcdn ⁡ ( x , k ) inverse-Jacobi-elliptic-dn 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{arcdn}\left(\NVar{x},\NVar{k}\right)}}

\aJacobielldnk@{\NVar{x}}{\NVar{k}}
Property / Symbols used: Q12009 / qualifier
 
xml-id: C22.S15.SS1.p1.m3acdec
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.m1mdec
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.m1mdec
Property / Symbols used
 
Property / Symbols used: Q11988 / rank
 
Normal rank
Property / Symbols used: Q11988 / qualifier
 
Defining formula:

k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}

k^{\prime}
Property / Symbols used: Q11988 / qualifier
 
xml-id: C22.S1.XMD5.m1bdec

Latest revision as of 15:28, 2 January 2020

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DLMF:22.15.E14
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    Statements

    Defining formula
    arcdn ⁡ ( x , k ) = ∫ x 1 d t ( 1 - t 2 ) ⁢ ( t 2 - k ′ 2 ) , inverse-Jacobi-elliptic-dn 𝑥 𝑘 superscript subscript 𝑥 1 𝑡 1 superscript 𝑡 2 superscript 𝑡 2 superscript superscript 𝑘 ′ 2 {\displaystyle{\displaystyle\operatorname{arcdn}\left(x,k\right)=\int_{x}^{1}% \frac{\mathrm{d}t}{\sqrt{(1-t^{2})(t^{2}-{k^{\prime}}^{2})}},}}
    0 references
    DLMF id
    DLMF:22.15.E14
    0 references
    constraint
    k ′ ≤ x ≤ 1 superscript 𝑘 ′ 𝑥 1 {\displaystyle{\displaystyle k^{\prime}\leq x\leq 1}}
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3acdec
    0 references
    Q12009
    Defining formula
    arcdn ⁡ ( x , k ) inverse-Jacobi-elliptic-dn 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{arcdn}\left(\NVar{x},\NVar{k}\right)}}
    xml-id
    C22.S15.SS1.p1.m3acdec
    0 references
    Q12003
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1mdec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1mdec
    0 references
    Q11988
    Defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C22.S1.XMD5.m1bdec
    0 references
     
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