DLMF:19.25.E3 (Q6507): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q11816 / rank
 
Normal rank
Property / Symbols used: Q11816 / qualifier
 
Defining formula:

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
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q11808 / qualifier
 
xml-id: C19.S1.XMD5.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11815 / rank
 
Normal rank
Property / Symbols used: Q11815 / qualifier
 
Defining formula:

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

k^{\prime}
Property / Symbols used: Q11815 / qualifier
 
xml-id: C19.S1.XMD6.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11809 / rank
 
Normal rank
Property / Symbols used: Q11809 / qualifier
 
Defining formula:

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

\alpha^{2}
Property / Symbols used: Q11809 / qualifier
 
xml-id: C19.S1.XMD7.m1adec

Latest revision as of 14:04, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:19.25.E3
No description defined

    Statements

    Defining formula
    Π ⁡ ( α 2 , k ) = 1 2 ⁢ π ⁢ R - 1 2 ⁡ ( 1 2 , - 1 2 , 1 ; k ′ 2 , 1 , 1 - α 2 ) , complete-elliptic-integral-third-kind-Pi superscript 𝛼 2 𝑘 1 2 𝜋 Carlson-integral-R 1 2 1 2 1 2 1 superscript superscript 𝑘 ′ 2 1 1 superscript 𝛼 2 {\displaystyle{\displaystyle\Pi\left(\alpha^{2},k\right)=\tfrac{1}{2}\pi R_{-% \frac{1}{2}}\left(\tfrac{1}{2},-\tfrac{1}{2},1;{k^{\prime}}^{2},1,1-\alpha^{2}% \right),}}
    0 references
    DLMF id
    DLMF:19.25.E3
    0 references
    Symbols used
    multivariate hypergeometric function
    Defining formula
    R - a ⁡ ( b 1 , … , b n ; z 1 , … , z n ) Carlson-integral-R 𝑎 subscript 𝑏 1 … subscript 𝑏 𝑛 subscript 𝑧 1 … subscript 𝑧 𝑛 {\displaystyle{\displaystyle R_{\NVar{-a}}\left(\NVar{b_{1}},\dots,\NVar{b_{n}% };\NVar{z_{1}},\dots,\NVar{z_{n}}\right)}}
    xml-id
    C19.S16.E9.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    Q11816
    Defining formula
    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
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1bdec
    0 references
    Q11815
    Defining formula
    k ′ superscript 𝑘 ′ {\displaystyle{\displaystyle k^{\prime}}}
    xml-id
    C19.S1.XMD6.m1bdec
    0 references
    Q11809
    Defining formula
    α 2 superscript 𝛼 2 {\displaystyle{\displaystyle\alpha^{2}}}
    xml-id
    C19.S1.XMD7.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6507&oldid=43251"