DLMF:19.34.E6 (Q6718): Difference between revisions

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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.m1bdec

Revision as of 14:26, 2 January 2020

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DLMF:19.34.E6
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    Statements

    Defining formula
    c 2 2 ⁢ π ⁢ M = ( r + 2 + r - 2 ) ⁢ R F ⁡ ( 0 , r + 2 , r - 2 ) - 4 ⁢ R G ⁡ ( 0 , r + 2 , r - 2 ) . speed-of-light 2 2 𝜋 𝑀 superscript subscript 𝑟 2 superscript subscript 𝑟 2 Carlson-integral-RF 0 superscript subscript 𝑟 2 superscript subscript 𝑟 2 4 Carlson-integral-RG 0 superscript subscript 𝑟 2 superscript subscript 𝑟 2 {\displaystyle{\displaystyle\frac{{c^{2}}}{2\pi}M=(r_{+}^{2}+r_{-}^{2})R_{F}% \left(0,r_{+}^{2},r_{-}^{2}\right)-4R_{G}\left(0,r_{+}^{2},r_{-}^{2}\right).}}
    0 references
    DLMF id
    DLMF:19.34.E6
    0 references
    Symbols used
    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.m2aadec
    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.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.m2abdec
    0 references
    Q11938
    Defining formula
    M 𝑀 {\displaystyle{\displaystyle M}}
    xml-id
    C19.S34.XMD1.m1bdec
    0 references
     
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