DLMF:4.35.E10 (Q1884)

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DLMF:4.35.E10
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    Statements

    Defining formula
    coth ⁡ u ± coth ⁡ v = sinh ⁡ ( v ± u ) sinh ⁡ u ⁢ sinh ⁡ v . plus-or-minus hyperbolic-cotangent 𝑢 hyperbolic-cotangent 𝑣 plus-or-minus 𝑣 𝑢 𝑢 𝑣 {\displaystyle{\displaystyle\coth u\pm\coth v=\frac{\sinh\left(v\pm u\right)}{% \sinh u\sinh v}.}}
    0 references
    DLMF id
    DLMF:4.35.E10
    0 references
    Symbols used
    hyperbolic cotangent function
    Defining formula
    coth ⁡ z hyperbolic-cotangent 𝑧 {\displaystyle{\displaystyle\coth\NVar{z}}}
    xml-id
    C4.S28.E7.m2aadec
    0 references
    hyperbolic sine function
    Defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2afdec
    0 references
     
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