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DLMF:19.25.E20 - MaRDI portal

DLMF:19.25.E20 (Q7220)

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DLMF:19.25.E20
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    Statements

    DLMF defining formula
    el1 ⁑ ( x , k c ) = R F ⁑ ( r , r + k c 2 , r + 1 ) , Bulirsch-integral-el-1 π‘₯ subscript π‘˜ 𝑐 Carlson-integral-RF π‘Ÿ π‘Ÿ superscript subscript π‘˜ 𝑐 2 π‘Ÿ 1 {\displaystyle{\displaystyle\mathrm{el1}\left(x,k_{c}\right)=R_{F}\left(r,r+k_% {c}^{2},r+1\right),}}
    0 references
    Symbols used
    Bulirsch’s incomplete elliptic integral of the first kind
    DLMF defining formula
    el1 ⁑ ( x , k c ) Bulirsch-integral-el-1 π‘₯ subscript π‘˜ 𝑐 {\displaystyle{\displaystyle\mathrm{el1}\left(\NVar{x},\NVar{k_{c}}\right)}}
    xml-id
    C19.S2.E15.m1adec
    0 references
    symmetric elliptic integral of first kind
    DLMF defining formula
    R F ⁑ ( x , y , z ) Carlson-integral-RF π‘₯ 𝑦 𝑧 {\displaystyle{\displaystyle R_{F}\left(\NVar{x},\NVar{y},\NVar{z}\right)}}
    xml-id
    C19.S16.E1.m2agdec
    0 references
    real or complex modulus
    DLMF defining formula
    k π‘˜ {\displaystyle{\displaystyle k}}
    xml-id
    C19.S1.XMD5.m1sdec
    0 references
    inverse
    DLMF defining formula
    r π‘Ÿ {\displaystyle{\displaystyle r}}
    xml-id
    C19.S25.XMD1.m1dec
    0 references

    Identifiers

     
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