DLMF:19.16.E23 (Q6341): Difference between revisions

From DRMF
Jump to navigation Jump to search
‎Created a new Item: Wikidata Toolkit example test item creation
 
‎Changed an Item: Add constraint
 
(2 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: multivariate hypergeometric function / rank
 
Normal rank
Property / Symbols used: multivariate hypergeometric function / qualifier
 
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)}}

\Carlsonmultivarhyper{\NVar{-a}}@{\NVar{b_{1}},\dots,\NVar{b_{n}}}{\NVar{z_{1}},\dots,\NVar{z_{n}}}
Property / Symbols used: multivariate hypergeometric function / qualifier
 
xml-id: C19.S16.E9.m2amdec
Property / Symbols used
 
Property / Symbols used: symmetric elliptic integral of second kind / rank
 
Normal rank
Property / Symbols used: symmetric elliptic integral of second kind / qualifier
 
Defining formula:

R G ⁡ ( x , y , z ) Carlson-integral-RG 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}

\CarlsonsymellintRG@{\NVar{x}}{\NVar{y}}{\NVar{z}}
Property / Symbols used: symmetric elliptic integral of second kind / qualifier
 
xml-id: C19.S16.E3.m2abdec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2addec

Latest revision as of 13:53, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:19.16.E23
No description defined

    Statements

    Defining formula
    R G ⁡ ( 0 , y , z ) = 1 4 ⁢ π ⁢ R 1 2 ⁡ ( 1 2 , 1 2 ; y , z ) = 1 4 ⁢ π ⁢ z ⁢ R - 1 2 ⁡ ( - 1 2 , 3 2 ; y , z ) . Carlson-integral-RG 0 𝑦 𝑧 1 4 𝜋 Carlson-integral-R 1 2 1 2 1 2 𝑦 𝑧 1 4 𝜋 𝑧 Carlson-integral-R 1 2 1 2 3 2 𝑦 𝑧 {\displaystyle{\displaystyle R_{G}\left(0,y,z\right)=\tfrac{1}{4}\pi R_{\frac{% 1}{2}}\left(\tfrac{1}{2},\tfrac{1}{2};y,z\right)=\tfrac{1}{4}\pi zR_{-\frac{1}% {2}}\left(-\tfrac{1}{2},\tfrac{3}{2};y,z\right).}}
    0 references
    DLMF id
    DLMF:19.16.E23
    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.m2amdec
    0 references
    symmetric elliptic integral of second kind
    Defining formula
    R G ⁡ ( x , y , z ) Carlson-integral-RG 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{G}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E3.m2abdec
    0 references
    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
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6341&oldid=41254"