DLMF:22.14.E7 (Q7082): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎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.m1fdec

Latest revision as of 15:23, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:22.14.E7
No description defined

    Statements

    Defining formula
    ∫ dc ⁡ ( x , k ) ⁢ d x = ln ⁡ ( nc ⁡ ( x , k ) + sc ⁡ ( x , k ) ) , Jacobi-elliptic-dc 𝑥 𝑘 𝑥 Jacobi-elliptic-nc 𝑥 𝑘 Jacobi-elliptic-sc 𝑥 𝑘 {\displaystyle{\displaystyle\int\operatorname{dc}\left(x,k\right)\mathrm{d}x=% \ln\left(\operatorname{nc}\left(x,k\right)+\operatorname{sc}\left(x,k\right)% \right),}}
    0 references
    DLMF id
    DLMF:22.14.E7
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    dc ⁡ ( z , k ) Jacobi-elliptic-dc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E8.m3adec
    0 references
    Jacobian elliptic function
    Defining formula
    nc ⁡ ( z , k ) Jacobi-elliptic-nc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{nc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m3adec
    0 references
    Jacobian elliptic function
    Defining formula
    sc ⁡ ( z , k ) Jacobi-elliptic-sc 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sc}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E9.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3afdec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
    0 references
    Q12003
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1fdec
    0 references
    Q11984
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1fdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7082&oldid=57357"