DLMF:9.7.E23 (Q2832): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2akdec
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
test:

ph phase {\displaystyle{\displaystyle\operatorname{ph}}}

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1akdec
Property / Symbols used
 
Property / Symbols used: Q11381 / rank
 
Normal rank
Property / Symbols used: Q11381 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11381 / qualifier
 
xml-id: C9.S1.XMD3.m1qdec
Property / Symbols used
 
Property / Symbols used: change of variable (locally) / rank
 
Normal rank
Property / Symbols used: change of variable (locally) / qualifier
 
test:

ζ 𝜁 {\displaystyle{\displaystyle\zeta}}

\zeta
Property / Symbols used: change of variable (locally) / qualifier
 
xml-id: C9.S7.XMD1.m1pdec
Property / Symbols used
 
Property / Symbols used: Q11392 / rank
 
Normal rank
Property / Symbols used: Q11392 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11392 / qualifier
 
xml-id: C9.S7.XMD10.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11391 / rank
 
Normal rank
Property / Symbols used: Q11391 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11391 / qualifier
 
xml-id: C9.S7.XMD11.m1ddec
Property / Symbols used
 
Property / Symbols used: remainder function (locally) / rank
 
Normal rank
Property / Symbols used: remainder function (locally) / qualifier
 
test:

R n subscript 𝑅 𝑛 {\displaystyle{\displaystyle R_{n}}}

R_{n}
Property / Symbols used: remainder function (locally) / qualifier
 
xml-id: C9.S7.XMD12.m1bdec
Property / Symbols used
 
Property / Symbols used: remainder function (locally) / rank
 
Normal rank
Property / Symbols used: remainder function (locally) / qualifier
 
test:

S n subscript 𝑆 𝑛 {\displaystyle{\displaystyle S_{n}}}

S_{n}
Property / Symbols used: remainder function (locally) / qualifier
 
xml-id: C9.S7.XMD13.m1bdec

Latest revision as of 13:37, 2 January 2020

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DLMF:9.7.E23
No description defined

    Statements

    test
    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),}}
    0 references
    DLMF id
    DLMF:9.7.E23
    0 references
    constraint
    | ph ⁡ z | ≤ 2 3 ⁢ π phase 𝑧 2 3 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{2}{3}\pi}}
    0 references
    Symbols used
    order not exceeding
    test
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ardec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2akdec
    0 references
    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1akdec
    0 references
    Q11381
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C9.S1.XMD3.m1qdec
    0 references
    change of variable (locally)
    test
    ζ 𝜁 {\displaystyle{\displaystyle\zeta}}
    xml-id
    C9.S7.XMD1.m1pdec
    0 references
    Q11392
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C9.S7.XMD10.m1bdec
    0 references
    Q11391
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C9.S7.XMD11.m1ddec
    0 references
    remainder function (locally)
    test
    R n subscript 𝑅 𝑛 {\displaystyle{\displaystyle R_{n}}}
    xml-id
    C9.S7.XMD12.m1bdec
    0 references
    remainder function (locally)
    test
    S n subscript 𝑆 𝑛 {\displaystyle{\displaystyle S_{n}}}
    xml-id
    C9.S7.XMD13.m1bdec
    0 references
     
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