DLMF:22.15.E22 (Q7117): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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.m1udec

Revision as of 15:30, 2 January 2020

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DLMF:22.15.E22
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    Statements

    Defining formula
    arcds ⁡ ( x , k ) = ∫ x ∞ d t ( t 2 + k 2 ) ⁢ ( t 2 - k ′ 2 ) , inverse-Jacobi-elliptic-ds 𝑥 𝑘 superscript subscript 𝑥 𝑡 superscript 𝑡 2 superscript 𝑘 2 superscript 𝑡 2 superscript superscript 𝑘 ′ 2 {\displaystyle{\displaystyle\operatorname{arcds}\left(x,k\right)=\int_{x}^{% \infty}\frac{\mathrm{d}t}{\sqrt{(t^{2}+k^{2})(t^{2}-{k^{\prime}}^{2})}},}}
    0 references
    DLMF id
    DLMF:22.15.E22
    0 references
    constraint
    k ′ ≤ x < ∞ superscript 𝑘 ′ 𝑥 {\displaystyle{\displaystyle k^{\prime}\leq x<\infty}}
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1akdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3akdec
    0 references
    Q12018
    Defining formula
    arcds ⁡ ( x , k ) inverse-Jacobi-elliptic-ds 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{arcds}\left(\NVar{x},\NVar{k}\right)}}
    xml-id
    C22.S15.SS1.p1.m10adec
    0 references
    Q12003
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1udec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1udec
    0 references
     
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