DLMF:19.34.E5 (Q6717): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11938 / rank
 
Normal rank
Property / Symbols used: Q11938 / qualifier
 
Defining formula:

M 𝑀 {\displaystyle{\displaystyle M}}

M
Property / Symbols used: Q11938 / qualifier
 
xml-id: C19.S34.XMD1.m1adec

Revision as of 14:26, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:19.34.E5
No description defined

    Statements

    Defining formula
    3 ⁢ c 2 8 ⁢ π ⁢ a ⁢ b ⁢ M = 3 ⁢ R F ⁡ ( 0 , r + 2 , r - 2 ) - 2 ⁢ r - 2 ⁢ R D ⁡ ( 0 , r + 2 , r - 2 ) , 3 speed-of-light 2 8 𝜋 𝑎 𝑏 𝑀 3 Carlson-integral-RF 0 superscript subscript 𝑟 2 superscript subscript 𝑟 2 2 superscript subscript 𝑟 2 Carlson-integral-RD 0 superscript subscript 𝑟 2 superscript subscript 𝑟 2 {\displaystyle{\displaystyle\frac{3{c^{2}}}{8\pi ab}M=3R_{F}\left(0,r_{+}^{2},% r_{-}^{2}\right)-2r_{-}^{2}R_{D}\left(0,r_{+}^{2},r_{-}^{2}\right),}}
    0 references
    DLMF id
    DLMF:19.34.E5
    0 references
    Symbols used
    elliptic integral symmetric in only two variables
    Defining formula
    R D ⁡ ( x , y , z ) Carlson-integral-RD 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{D}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E5.m2adec
    0 references
    symmetric elliptic integral of first kind
    Defining formula
    R F ⁡ ( x , y , z ) Carlson-integral-RF 𝑥 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E1.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.m2aadec
    0 references
    Q11938
    Defining formula
    M 𝑀 {\displaystyle{\displaystyle M}}
    xml-id
    C19.S34.XMD1.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6717&oldid=47146"