DLMF:19.9.E7 (Q6250)

From DRMF
Revision as of 13:45, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:19.9.E7
No description defined

    Statements

    Defining formula
    ( 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
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    Q11600
    Defining formula
    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
    Defining formula
    E ⁡ ( k ) complete-elliptic-integral-second-kind-E 𝑘 {\displaystyle{\displaystyle E\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m2acdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6250&oldid=39714"