DLMF:22.14.E13 (Q7088): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2ahdec

Revision as of 15:25, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:22.14.E13
No description defined

    Statements

    Defining formula
    ∫ d x sn ⁡ ( x , k ) = ln ⁡ ( sn ⁡ ( x , k ) cn ⁡ ( x , k ) + dn ⁡ ( x , k ) ) , 𝑥 Jacobi-elliptic-sn 𝑥 𝑘 Jacobi-elliptic-sn 𝑥 𝑘 Jacobi-elliptic-cn 𝑥 𝑘 Jacobi-elliptic-dn 𝑥 𝑘 {\displaystyle{\displaystyle\int\frac{\mathrm{d}x}{\operatorname{sn}\left(x,k% \right)}=\ln\left(\frac{\operatorname{sn}\left(x,k\right)}{\operatorname{cn}% \left(x,k\right)+\operatorname{dn}\left(x,k\right)}\right),}}
    0 references
    DLMF id
    DLMF:22.14.E13
    0 references
    Symbols used
    Jacobian elliptic function
    Defining formula
    cn ⁡ ( z , k ) Jacobi-elliptic-cn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{cn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E5.m2abdec
    0 references
    Jacobian elliptic function
    Defining formula
    dn ⁡ ( z , k ) Jacobi-elliptic-dn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{dn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E6.m2acdec
    0 references
    Jacobian elliptic function
    Defining formula
    sn ⁡ ( z , k ) Jacobi-elliptic-sn 𝑧 𝑘 {\displaystyle{\displaystyle\operatorname{sn}\left(\NVar{z},\NVar{k}\right)}}
    xml-id
    C22.S2.E4.m2abdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aldec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aldec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2ahdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7088&oldid=57587"