DLMF:22.15.E20 (Q7115): Difference between revisions

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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.m1sdec
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.m1sdec
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.m1fdec

Latest revision as of 15:30, 2 January 2020

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DLMF:22.15.E20
No description defined

    Statements

    Defining formula
    arcsc ⁡ ( x , k ) = ∫ 0 x d t ( 1 + t 2 ) ⁢ ( 1 + k ′ 2 ⁢ t 2 ) , inverse-Jacobi-elliptic-sc 𝑥 𝑘 superscript subscript 0 𝑥 𝑡 1 superscript 𝑡 2 1 superscript superscript 𝑘 ′ 2 superscript 𝑡 2 {\displaystyle{\displaystyle\operatorname{arcsc}\left(x,k\right)=\int_{0}^{x}% \frac{\mathrm{d}t}{\sqrt{(1+t^{2})(1+{k^{\prime}}^{2}t^{2})}},}}
    0 references
    DLMF id
    DLMF:22.15.E20
    0 references
    constraint
    - ∞ < x < ∞ 𝑥 {\displaystyle{\displaystyle-\infty<x<\infty}}
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aidec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aidec
    0 references
    Q12016
    Defining formula
    arcsc ⁡ ( x , k ) inverse-Jacobi-elliptic-sc 𝑥 𝑘 {\displaystyle{\displaystyle\operatorname{arcsc}\left(\NVar{x},\NVar{k}\right)}}
    xml-id
    C22.S15.SS1.p1.m6adec
    0 references
    Q12003
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1sdec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1sdec
    0 references
    Q11988
    Defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C22.S1.XMD5.m1fdec
    0 references
     
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