DLMF:19.21.E5 (Q6423): Difference between revisions

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‎Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2aadec

Latest revision as of 13:58, 2 January 2020

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DLMF:19.21.E5
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    Statements

    Defining formula
    2 ⁢ R G ⁡ ( 0 , z - 1 , z ) = 2 ⁢ R G ⁡ ( 0 , 1 - z , 1 ) ± i ⁢ 2 ⁢ R G ⁡ ( 0 , z , 1 ) + ( z - 1 ) ⁢ R F ⁡ ( 0 , 1 - z , 1 ) ∓ i ⁢ z ⁢ R F ⁡ ( 0 , z , 1 ) . 2 Carlson-integral-RG 0 𝑧 1 𝑧 minus-or-plus plus-or-minus 2 Carlson-integral-RG 0 1 𝑧 1 imaginary-unit 2 Carlson-integral-RG 0 𝑧 1 𝑧 1 Carlson-integral-RF 0 1 𝑧 1 imaginary-unit 𝑧 Carlson-integral-RF 0 𝑧 1 {\displaystyle{\displaystyle 2R_{G}\left(0,z-1,z\right)=2R_{G}\left(0,1-z,1% \right)\pm\mathrm{i}2R_{G}\left(0,z,1\right)+(z-1)R_{F}\left(0,1-z,1\right)\mp% \mathrm{i}zR_{F}\left(0,z,1\right).}}
    0 references
    DLMF id
    DLMF:19.21.E5
    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.m2addec
    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.m2aadec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
     
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