DLMF:19.7.E1 (Q6181): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11821 / rank
 
Normal rank
Property / Symbols used: Q11821 / qualifier
 
test:

K ′ ⁡ ( k ) complementary-complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle{K^{\prime}}\left(\NVar{k}\right)}}

\ccompellintKk@{\NVar{k}}
Property / Symbols used: Q11821 / qualifier
 
xml-id: C19.S2.E9.m1adec
Property / Symbols used
 
Property / Symbols used: Q11822 / rank
 
Normal rank
Property / Symbols used: Q11822 / qualifier
 
test:

E ′ ⁡ ( k ) complementary-complete-elliptic-integral-second-kind-E 𝑘 {\displaystyle{\displaystyle{E^{\prime}}\left(\NVar{k}\right)}}

\ccompellintEk@{\NVar{k}}
Property / Symbols used: Q11822 / qualifier
 
xml-id: C19.S2.E9.m2adec
Property / Symbols used
 
Property / Symbols used: Q11600 / rank
 
Normal rank
Property / Symbols used: Q11600 / qualifier
 
test:

K ⁡ ( k ) complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}

\compellintKk@{\NVar{k}}
Property / Symbols used: Q11600 / qualifier
 
xml-id: C19.S2.E8.m1adec
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.m2adec
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.m1dec

Latest revision as of 12:41, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:19.7.E1
No description defined

    Statements

    test
    E ⁡ ( k ) ⁢ K ′ ⁡ ( k ) + E ′ ⁡ ( k ) ⁢ K ⁡ ( k ) - K ⁡ ( k ) ⁢ K ′ ⁡ ( k ) = 1 2 ⁢ π . complete-elliptic-integral-second-kind-E 𝑘 complementary-complete-elliptic-integral-first-kind-K 𝑘 complementary-complete-elliptic-integral-second-kind-E 𝑘 complete-elliptic-integral-first-kind-K 𝑘 complete-elliptic-integral-first-kind-K 𝑘 complementary-complete-elliptic-integral-first-kind-K 𝑘 1 2 𝜋 {\displaystyle{\displaystyle E\left(k\right){K^{\prime}}\left(k\right)+{E^{% \prime}}\left(k\right)K\left(k\right)-K\left(k\right){K^{\prime}}\left(k\right% )=\tfrac{1}{2}\pi.}}
    0 references
    DLMF id
    DLMF:19.7.E1
    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.m2adec
    0 references
    Q11821
    test
    K ′ ⁡ ( k ) complementary-complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle{K^{\prime}}\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E9.m1adec
    0 references
    Q11822
    test
    E ′ ⁡ ( k ) complementary-complete-elliptic-integral-second-kind-E 𝑘 {\displaystyle{\displaystyle{E^{\prime}}\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E9.m2adec
    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.m1adec
    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.m2adec
    0 references
    Q11808
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1dec
    0 references
     
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