DLMF:1.2.E16} (Q45)

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DLMF:1.2.E16}
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    Statements

    Defining formula
    f ⁢ ( x ) ( x - α 1 ) m 1 ⁢ ( x - α 2 ) m 2 ⁢ ⋯ ⁢ ( x - α n ) m n = f 1 ⁢ ( x ) ( x - α 1 ) m 1 + f 2 ⁢ ( x ) ( x - α 2 ) m 2 + ⋯ + f n ⁢ ( x ) ( x - α n ) m n . 𝑓 𝑥 superscript 𝑥 subscript 𝛼 1 subscript 𝑚 1 superscript 𝑥 subscript 𝛼 2 subscript 𝑚 2 ⋯ superscript 𝑥 subscript 𝛼 𝑛 subscript 𝑚 𝑛 subscript 𝑓 1 𝑥 superscript 𝑥 subscript 𝛼 1 subscript 𝑚 1 subscript 𝑓 2 𝑥 superscript 𝑥 subscript 𝛼 2 subscript 𝑚 2 ⋯ subscript 𝑓 𝑛 𝑥 superscript 𝑥 subscript 𝛼 𝑛 subscript 𝑚 𝑛 {\displaystyle{\displaystyle\frac{f(x)}{(x-\alpha_{1})^{m_{1}}(x-\alpha_{2})^{% m_{2}}\cdots(x-\alpha_{n})^{m_{n}}}=\frac{f_{1}(x)}{(x-\alpha_{1})^{m_{1}}}+% \frac{f_{2}(x)}{(x-\alpha_{2})^{m_{2}}}+\cdots+\frac{f_{n}(x)}{(x-\alpha_{n})^% {m_{n}}}.}}
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    DLMF id
    DLMF:1.2.E16}
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    comment
    Warning: Falling back to standard tex;
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    Symbols used
    Q10761
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C1.S1.XMD6.m1bdec
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