DLMF:19.6.E3 (Q6146): Difference between revisions

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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.m1abdec
Property / Symbols used
 
Property / Symbols used: Q11816 / rank
 
Normal rank
Property / Symbols used: Q11816 / qualifier
 
test:

Π ⁡ ( α 2 , k ) complete-elliptic-integral-third-kind-Pi superscript 𝛼 2 𝑘 {\displaystyle{\displaystyle\Pi\left(\NVar{\alpha}^{2},\NVar{k}\right)}}

\compellintPik@{\NVar{\alpha}^{2}}{\NVar{k}}
Property / Symbols used: Q11816 / qualifier
 
xml-id: C19.S2.E8.m4aadec
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.m1adec
Property / Symbols used
 
Property / Symbols used: Q11809 / rank
 
Normal rank
Property / Symbols used: Q11809 / qualifier
 
test:

α 2 superscript 𝛼 2 {\displaystyle{\displaystyle\alpha^{2}}}

\alpha^{2}
Property / Symbols used: Q11809 / qualifier
 
xml-id: C19.S1.XMD7.m1dec

Latest revision as of 12:40, 2 January 2020

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DLMF:19.6.E3
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    Statements

    test
    Π ⁡ ( α 2 , 0 ) = π / ( 2 ⁢ 1 - α 2 ) , Π ⁡ ( 0 , k ) = K ⁡ ( k ) , formulae-sequence complete-elliptic-integral-third-kind-Pi superscript 𝛼 2 0 𝜋 2 1 superscript 𝛼 2 complete-elliptic-integral-third-kind-Pi 0 𝑘 complete-elliptic-integral-first-kind-K 𝑘 {\displaystyle{\displaystyle\Pi\left(\alpha^{2},0\right)=\pi/(2\sqrt{1-\alpha^% {2}}),\quad\Pi\left(0,k\right)=K\left(k\right),}}
    0 references
    DLMF id
    DLMF:19.6.E3
    0 references
    constraint
    - ∞ < α 2 < 1 superscript 𝛼 2 1 {\displaystyle{\displaystyle-\infty<\alpha^{2}<1}}
    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.m2abdec
    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.m1abdec
    0 references
    Q11816
    test
    Π ⁡ ( α 2 , k ) complete-elliptic-integral-third-kind-Pi superscript 𝛼 2 𝑘 {\displaystyle{\displaystyle\Pi\left(\NVar{\alpha}^{2},\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m4aadec
    0 references
    Q11808
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1adec
    0 references
    Q11809
    test
    α 2 superscript 𝛼 2 {\displaystyle{\displaystyle\alpha^{2}}}
    xml-id
    C19.S1.XMD7.m1dec
    0 references
     
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