DLMF:19.9.E7 (Q6250): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older edit
imported>Admin
imported>Admin
 
(One intermediate revision by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q11808 / rank
 
Normal rank
Property / Symbols used: Q11808 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11808 / qualifier
 
xml-id: C19.S1.XMD5.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11815 / rank
 
Normal rank
Property / Symbols used: Q11815 / qualifier
 
test:

k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}

k^{\prime}
Property / Symbols used: Q11815 / qualifier
 
xml-id: C19.S1.XMD6.m1fdec

Latest revision as of 12:45, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:19.9.E7
No description defined

    Statements

    test
    ( 1 - 1 4 ⁢ k 2 ) - 1 / 2 < 4 π ⁢ k 2 ⁢ ( E ⁡ ( k ) - k ′ 2 ⁢ K ⁡ ( k ) ) < min ⁡ ( ( k ′ ) - 1 / 4 , 4 / π ) , superscript 1 1 4 superscript 𝑘 2 1 2 4 𝜋 superscript 𝑘 2 complete-elliptic-integral-second-kind-E 𝑘 superscript superscript 𝑘 ′ 2 complete-elliptic-integral-first-kind-K 𝑘 superscript superscript 𝑘 ′ 1 4 4 𝜋 {\displaystyle{\displaystyle(1-\tfrac{1}{4}k^{2})^{-1/2}<\frac{4}{\pi k^{2}}(E% \left(k\right)-{k^{\prime}}^{2}K\left(k\right))<\min((k^{\prime})^{-1/4},4/\pi% ),}}
    0 references
    DLMF id
    DLMF:19.9.E7
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    Q11600
    test
    K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1aedec
    0 references
    Q11601
    test
    E ⁡ ( k ) complete-elliptic-integral-second-kind-E 𝑘 {\displaystyle{\displaystyle E\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m2acdec
    0 references
    Q11808
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1fdec
    0 references
    Q11815
    test
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C19.S1.XMD6.m1fdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q6250&oldid=35642"