DLMF:1.12.E19 (Q449)

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DLMF:1.12.E19
No description defined

    Statements

    Defining formula
    ∑ k = 0 n c k ⁢ x k = c 0 + c 1 ⁢ x 1 - ( c 2 / c 1 ) ⁢ x 1 + ( c 2 / c 1 ) ⁢ x - ( c 3 / c 2 ) ⁢ x 1 + ( c 3 / c 2 ) ⁢ x - ⋯ ( c n / c n - 1 ) ⁢ x 1 + ( c n / c n - 1 ) ⁢ x , subscript superscript 𝑛 𝑘 0 subscript 𝑐 𝑘 superscript 𝑥 𝑘 subscript 𝑐 0 continued-fraction subscript 𝑐 1 𝑥 1 continued-fraction subscript 𝑐 2 subscript 𝑐 1 𝑥 1 subscript 𝑐 2 subscript 𝑐 1 𝑥 continued-fraction subscript 𝑐 3 subscript 𝑐 2 𝑥 1 subscript 𝑐 3 subscript 𝑐 2 𝑥 ⋯ continued-fraction subscript 𝑐 𝑛 subscript 𝑐 𝑛 1 𝑥 1 subscript 𝑐 𝑛 subscript 𝑐 𝑛 1 𝑥 {\displaystyle{\displaystyle\sum^{n}_{k=0}c_{k}x^{k}=c_{0}+\cfrac{c_{1}x}{1-% \cfrac{(\ifrac{c_{2}}{c_{1}})x}{1+(\ifrac{c_{2}}{c_{1}})x-\cfrac{(\ifrac{c_{3}% }{c_{2}})x}{1+(\ifrac{c_{3}}{c_{2}})x-\cdots\cfrac{(\ifrac{c_{n}}{c_{n-1}})x}{% 1+(\ifrac{c_{n}}{c_{n-1}})x}}}},}}
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    DLMF id
    DLMF:1.12.E19
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    comment
    Warning: Falling back to standard tex;
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    constraint
    n = 0 , 1 , 2 , … 𝑛 0 1 2 … {\displaystyle{\displaystyle n=0,1,2,\dots}}
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    Symbols used
    Q10756
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C1.S1.XMD4.m1edec
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    Q10757
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1mdec
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