DLMF:26.5.E2 (Q7797)

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DLMF:26.5.E2
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    Statements

    Defining formula
    ∑ n = 0 ∞ C ⁡ ( n ) ⁢ x n = 1 - 1 - 4 ⁢ x 2 ⁢ x , superscript subscript 𝑛 0 Catalan-number 𝑛 superscript 𝑥 𝑛 1 1 4 𝑥 2 𝑥 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}C\left(n\right)x^{n}=\frac{1-% \sqrt{1-4x}}{2x},}}
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    DLMF id
    DLMF:26.5.E2
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    constraint
    | x | < 1 4 𝑥 1 4 {\displaystyle{\displaystyle|x|<\tfrac{1}{4}}}
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    Symbols used
    Catalan number
    Defining formula
    C ⁡ ( n ) Catalan-number 𝑛 {\displaystyle{\displaystyle C\left(\NVar{n}\right)}}
    xml-id
    C26.S5.E1.m2abdec
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    Q12173
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C26.S1.XMD1.m1dec
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    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1bdec
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