DLMF:19.30.E9 (Q6684)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:19.30.E9
No description defined

    Statements

    Defining formula
    s = 1 2 ⁢ I ⁢ ( 𝐞 1 ) = - 1 3 ⁢ a 2 ⁢ b 2 ⁢ R D ⁡ ( r , r + b 2 + a 2 , r + b 2 ) + y ⁢ r + b 2 + a 2 r + b 2 , 𝑠 1 2 𝐼 subscript 𝐞 1 1 3 superscript 𝑎 2 superscript 𝑏 2 Carlson-integral-RD 𝑟 𝑟 superscript 𝑏 2 superscript 𝑎 2 𝑟 superscript 𝑏 2 𝑦 𝑟 superscript 𝑏 2 superscript 𝑎 2 𝑟 superscript 𝑏 2 {\displaystyle{\displaystyle s=\tfrac{1}{2}I(\mathbf{e}_{1})=-\tfrac{1}{3}a^{2% }b^{2}R_{D}\left(r,r+b^{2}+a^{2},r+b^{2}\right)+y\sqrt{\frac{r+b^{2}+a^{2}}{r+% b^{2}}},}}
    0 references
    DLMF id
    DLMF:19.30.E9
    0 references
    constraint
    r = b 4 / y 2 𝑟 superscript 𝑏 4 superscript 𝑦 2 {\displaystyle{\displaystyle r=b^{4}/y^{2}}}
    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.m2aadec
    0 references
    Q11906
    Defining formula
    I ⁢ ( 𝐦 ) 𝐼 𝐦 {\displaystyle{\displaystyle I(\mathbf{m})}}
    xml-id
    C19.S29.XMD13.m1dec
    0 references
    Q11917
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C19.S30.XMD3.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6684&oldid=46547"