DLMF:19.9.E8 (Q6251): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11601 / rank
 
Normal rank
Property / Symbols used: Q11601 / qualifier
 
test:

E ( k ) complete-elliptic-integral-second-kind-E 𝑘 {\displaystyle{\displaystyle E\left(\NVar{k}\right)}}

\compellintEk@{\NVar{k}}
Property / Symbols used: Q11601 / qualifier
 
xml-id: C19.S2.E8.m2addec
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.m1gdec
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.m1gdec

Latest revision as of 12:45, 2 January 2020

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DLMF:19.9.E8
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    Statements

    k < E ( k ) K ( k ) < ( 1 + k 2 ) 2 . superscript 𝑘 complete-elliptic-integral-second-kind-E 𝑘 complete-elliptic-integral-first-kind-K 𝑘 superscript 1 superscript 𝑘 2 2 {\displaystyle{\displaystyle k^{\prime}<\frac{E\left(k\right)}{K\left(k\right)% }<\left(\frac{1+k^{\prime}}{2}\right)^{2}.}}
    0 references
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    K ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    C19.S2.E8.m1afdec
    0 references
    E ( k ) complete-elliptic-integral-second-kind-E 𝑘 {\displaystyle{\displaystyle E\left(\NVar{k}\right)}}
    C19.S2.E8.m2addec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C19.S1.XMD5.m1gdec
    0 references
    k superscript 𝑘 {\displaystyle{\displaystyle k^{\prime}}}
    C19.S1.XMD6.m1gdec
    0 references