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DLMF:22.16.E34 - MaRDI portal

DLMF:22.16.E34 (Q7847)

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DLMF:22.16.E34
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    Statements

    DLMF defining formula
    Z โก ( x + 2 โข K | k ) = Z โก ( x | k ) . Jacobi-Zeta ๐‘ฅ 2 ๐พ ๐‘˜ Jacobi-Zeta ๐‘ฅ ๐‘˜ {\displaystyle{\displaystyle\mathrm{Z}\left(x+2K|k\right)=\mathrm{Z}\left(x|k% \right).}}
    0 references
    Symbols used
    Jacobiโ€™s zeta function
    DLMF defining formula
    Z โก ( x | k ) Jacobi-Zeta ๐‘ฅ ๐‘˜ {\displaystyle{\displaystyle\mathrm{Z}\left(\NVar{x}|\NVar{k}\right)}}
    xml-id
    C22.S16.E32.m2abdec
    0 references
    Legendreโ€™s complete elliptic integral of the first kind
    DLMF defining formula
    K โก ( k ) complete-elliptic-integral-first-kind-K ๐‘˜ {\displaystyle{\displaystyle K\left(\NVar{k}\right)}}
    xml-id
    C19.S2.E8.m1ahdec
    0 references
    real
    DLMF defining formula
    x ๐‘ฅ {\displaystyle{\displaystyle x}}
    xml-id
    C22.S1.XMD1.m1agdec
    0 references
    modulus
    DLMF defining formula
    k ๐‘˜ {\displaystyle{\displaystyle k}}
    xml-id
    C22.S1.XMD4.m1aedec
    0 references

    Identifiers

     
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