DLMF:29.6.E45 (Q8677): 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
Property / Symbols used
 
Property / Symbols used: Q12364 / rank
 
Normal rank
Property / Symbols used: Q12364 / qualifier
 
Defining formula:

𝐸𝑠 ν m ( z , k 2 ) Lame-Es 𝑚 𝜈 𝑧 superscript 𝑘 2 {\displaystyle{\displaystyle\mathit{Es}^{\NVar{m}}_{\NVar{\nu}}\left(\NVar{z},% \NVar{k^{2}}\right)}}

\LameEs{\NVar{m}}{\NVar{\nu}}@{\NVar{z}}{\NVar{k^{2}}}
Property / Symbols used: Q12364 / qualifier
 
xml-id: C29.S3.SS4.p1.m6abdec

Revision as of 01:18, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:29.6.E45
No description defined

    Statements

    p = 0 B 2 p + 1 D 2 p + 1 = 4 π 0 K ( 𝐸𝑠 ν 2 m + 1 ( x , k 2 ) ) 2 d x . superscript subscript 𝑝 0 subscript 𝐵 2 𝑝 1 subscript 𝐷 2 𝑝 1 4 𝜋 superscript subscript 0 complete-elliptic-integral-first-kind-K 𝑘 superscript Lame-Es 2 𝑚 1 𝜈 𝑥 superscript 𝑘 2 2 𝑥 {\displaystyle{\displaystyle\sum_{p=0}^{\infty}B_{2p+1}D_{2p+1}=\frac{4}{\pi}% \int_{0}^{K}\left(\mathit{Es}^{2m+1}_{\nu}\left(x,k^{2}\right)\right)^{2}% \mathrm{d}x.}}
    0 references
    DLMF:29.6.E45
    0 references
    𝐸𝑠 ν m ( z , k 2 ) Lame-Es 𝑚 𝜈 𝑧 superscript 𝑘 2 {\displaystyle{\displaystyle\mathit{Es}^{\NVar{m}}_{\NVar{\nu}}\left(\NVar{z},% \NVar{k^{2}}\right)}}
    C29.S3.SS4.p1.m6abdec
    0 references