DLMF:9.7.E23 (Q2832)

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DLMF:9.7.E23
No description defined

    Statements

    Defining formula
    R m , n ⁢ ( z ) , S m , n ⁢ ( z ) = O ⁡ ( e - 2 ⁢ | ζ | ⁢ ζ - m ) , subscript 𝑅 𝑚 𝑛 𝑧 subscript 𝑆 𝑚 𝑛 𝑧 Big-O superscript 𝑒 2 𝜁 superscript 𝜁 𝑚 {\displaystyle{\displaystyle R_{m,n}(z),S_{m,n}(z)=O\left(e^{-2|\zeta|}\zeta^{% -m}\right),}}
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    DLMF id
    DLMF:9.7.E23
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    constraint
    | ph ⁡ z | ≤ 2 3 ⁢ π phase 𝑧 2 3 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{2}{3}\pi}}
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    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
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    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ardec
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    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2akdec
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    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1akdec
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    Q11381
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1qdec
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    change of variable (locally)
    Defining formula
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C9.S7.XMD1.m1pdec
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    Q11392
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C9.S7.XMD10.m1bdec
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    Q11391
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C9.S7.XMD11.m1ddec
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    remainder function (locally)
    Defining formula
    R n subscript 𝑅 𝑛 {\displaystyle{\displaystyle R_{n}}}
    xml-id
    C9.S7.XMD12.m1bdec
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