DLMF:23.14.E3 (Q7329): Difference between revisions

From DRMF
Jump to navigation Jump to search
‎Created a new Item: Wikidata Toolkit example test item creation
 
‎Changed an Item: Add constraint
 
(6 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: DLMF:23.2.E4 / rank
 
Normal rank
Property / Symbols used: DLMF:23.2.E4 / qualifier
 
Defining formula:

℘ ⁡ ( z ) Weierstrass-P-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\wp\left(\NVar{z}\right)}}

\Weierstrassplatt@@{\NVar{z}}{\NVar{\mathbb{L}}}
Property / Symbols used: DLMF:23.2.E4 / qualifier
 
xml-id: C23.S2.E4.m2abdec
Property / Symbols used
 
Property / Symbols used: Q12054 / rank
 
Normal rank
Property / Symbols used: Q12054 / qualifier
 
Defining formula:

g j ⁡ Weierstrass-invariants-on-lattice 𝑗 𝕃 {\displaystyle{\displaystyle g_{\NVar{j}}}}

\Weierstrassinvarlatt{\NVar{j}}@@{\NVar{\mathbb{L}}}
Property / Symbols used: Q12054 / qualifier
 
xml-id: C23.S3.EGx1.m1aadec
Property / Symbols used
 
Property / Symbols used: DLMF:23.2.E5 / rank
 
Normal rank
Property / Symbols used: DLMF:23.2.E5 / qualifier
 
Defining formula:

ζ ⁡ ( z ) Weierstrass-zeta-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\zeta\left(\NVar{z}\right)}}

\Weierstrasszetalatt@@{\NVar{z}}{\NVar{\mathbb{L}}}
Property / Symbols used: DLMF:23.2.E5 / qualifier
 
xml-id: C23.S2.E5.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1abdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3abdec
Property / Symbols used
 
Property / Symbols used: Q12055 / rank
 
Normal rank
Property / Symbols used: Q12055 / qualifier
 
Defining formula:

𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}}

\mathbb{L}
Property / Symbols used: Q12055 / qualifier
 
xml-id: C23.S1.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12056 / rank
 
Normal rank
Property / Symbols used: Q12056 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q12056 / qualifier
 
xml-id: C23.S1.XMD7.m1bdec

Latest revision as of 16:03, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:23.14.E3
No description defined

    Statements

    Defining formula
    ∫ ℘ 3 ⁡ ( z ) ⁢ d z = 1 120 ⁢ ℘ ′′′ ⁡ ( z ) - 3 20 ⁢ g 2 ⁡ ⁢ ζ ⁡ ( z ) + 1 10 ⁢ g 3 ⁡ ⁢ z . Weierstrass-P-on-lattice 3 𝑧 𝕃 𝑧 1 120 diffop Weierstrass-P-on-lattice 3 𝑧 𝕃 3 20 Weierstrass-invariants-on-lattice 2 𝕃 Weierstrass-zeta-on-lattice 𝑧 𝕃 1 10 Weierstrass-invariants-on-lattice 3 𝕃 𝑧 {\displaystyle{\displaystyle\int{\wp^{3}}\left(z\right)\mathrm{d}z=\frac{1}{12% 0}\wp'''\left(z\right)-\frac{3}{20}g_{2}\zeta\left(z\right)+\frac{1}{10}g_{3}z% .}}
    0 references
    DLMF id
    DLMF:23.14.E3
    0 references
    Symbols used
    DLMF:23.2.E4
    Defining formula
    ℘ ⁡ ( z ) Weierstrass-P-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\wp\left(\NVar{z}\right)}}
    xml-id
    C23.S2.E4.m2abdec
    0 references
    Q12054
    Defining formula
    g j ⁡ Weierstrass-invariants-on-lattice 𝑗 𝕃 {\displaystyle{\displaystyle g_{\NVar{j}}}}
    xml-id
    C23.S3.EGx1.m1aadec
    0 references
    DLMF:23.2.E5
    Defining formula
    ζ ⁡ ( z ) Weierstrass-zeta-on-lattice 𝑧 𝕃 {\displaystyle{\displaystyle\zeta\left(\NVar{z}\right)}}
    xml-id
    C23.S2.E5.m2aadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
    0 references
    Q12055
    Defining formula
    𝕃 𝕃 {\displaystyle{\displaystyle\mathbb{L}}}
    xml-id
    C23.S1.XMD1.m1bdec
    0 references
    Q12056
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C23.S1.XMD7.m1bdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7329&oldid=62400"