DLMF:1.9.E21 (Q295)

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DLMF:1.9.E21
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    Statements

    test
    z n = ( x n - ( n 2 ) ⁢ x n - 2 ⁢ y 2 + ( n 4 ) ⁢ x n - 4 ⁢ y 4 - ⋯ ) + i ⁢ ( ( n 1 ) ⁢ x n - 1 ⁢ y - ( n 3 ) ⁢ x n - 3 ⁢ y 3 + ⋯ ) , superscript 𝑧 𝑛 superscript 𝑥 𝑛 binomial 𝑛 2 superscript 𝑥 𝑛 2 superscript 𝑦 2 binomial 𝑛 4 superscript 𝑥 𝑛 4 superscript 𝑦 4 ⋯ 𝑖 binomial 𝑛 1 superscript 𝑥 𝑛 1 𝑦 binomial 𝑛 3 superscript 𝑥 𝑛 3 superscript 𝑦 3 ⋯ {\displaystyle{\displaystyle z^{n}=\left(x^{n}-\genfrac{(}{)}{0.0pt}{}{n}{2}x^% {n-2}y^{2}+\genfrac{(}{)}{0.0pt}{}{n}{4}x^{n-4}y^{4}-\cdots\right)+i\left(% \genfrac{(}{)}{0.0pt}{}{n}{1}x^{n-1}y-\genfrac{(}{)}{0.0pt}{}{n}{3}x^{n-3}y^{3% }+\cdots\right),}}
    0 references
    DLMF id
    DLMF:1.9.E21
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    constraint
    n = 1 , 2 , … 𝑛 1 2 … {\displaystyle{\displaystyle n=1,2,\dots}}
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    Symbols used
    Q10754
    test
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1adec
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    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2agdec
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    Q10760
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C1.S1.XMD1.m1odec
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    Q10757
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1adec
    0 references
     
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