DLMF:22.15.E19 (Q7114): Difference between revisions

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‎Changed an Item: Add constraint
 
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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.m1rdec
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.m1rdec
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.m1edec

Latest revision as of 15:29, 2 January 2020

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DLMF:22.15.E19
No description defined

    Statements

    Defining formula
    arcnc ⁡ ( x , k ) = ∫ 1 x d t ( t 2 - 1 ) ⁢ ( k 2 + k ′ 2 ⁢ t 2 ) , inverse-Jacobi-elliptic-nc 𝑥 𝑘 superscript subscript 1 𝑥 𝑡 superscript 𝑡 2 1 superscript 𝑘 2 superscript superscript 𝑘 ′ 2 superscript 𝑡 2 {\displaystyle{\displaystyle\operatorname{arcnc}\left(x,k\right)=\int_{1}^{x}% \frac{\mathrm{d}t}{\sqrt{(t^{2}-1)(k^{2}+{k^{\prime}}^{2}t^{2})}},}}
    0 references
    DLMF id
    DLMF:22.15.E19
    0 references
    constraint
    1 ≤ x < ∞ 1 𝑥 {\displaystyle{\displaystyle 1\leq x<\infty}}
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1ahdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3ahdec
    0 references
    Q12015
    Defining formula
    arcnc ⁡ ( x , k ) inverse-Jacobi-elliptic-nc 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{arcnc}\left(\NVar{x},\NVar{k}\right)}}
    xml-id
    C22.S15.SS1.p1.m8adec
    0 references
    Q12003
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1rdec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1rdec
    0 references
    Q11988
    Defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C22.S1.XMD5.m1edec
    0 references
     
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