DLMF:2.11.E23 (Q1048): 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.m2apdec
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.m1aadec
Property / Symbols used
 
Property / Symbols used: Q11141 / rank
 
Normal rank
Property / Symbols used: Q11141 / qualifier
 
test:

R n ( j ) ⁢ ( z ) superscript subscript 𝑅 𝑛 𝑗 𝑧 {\displaystyle{\displaystyle R_{n}^{(j)}(z)}}

R_{n}^{(j)}(z)
Property / Symbols used: Q11141 / qualifier
 
xml-id: C2.S11.XMD10.m1ddec
Property / Symbols used
 
Property / Symbols used: Q11144 / rank
 
Normal rank
Property / Symbols used: Q11144 / qualifier
 
test:

δ 𝛿 {\displaystyle{\displaystyle\delta}}

\delta
Property / Symbols used: Q11144 / qualifier
 
xml-id: C2.S11.XMD5.m1adec

Latest revision as of 16:42, 1 January 2020

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DLMF:2.11.E23
No description defined

    Statements

    test
    R m , n ( 2 ) ⁢ ( z ) = { O ⁡ ( e - | z | + z ⁢ z - m ) , 0 ≤ ph ⁡ z ≤ 2 ⁢ π , O ⁡ ( z - m ) , - 3 2 ⁢ π + δ ≤ ph ⁡ z ≤ 0 ⁢  and  ⁢ 2 ⁢ π ≤ ph ⁡ z ≤ 7 2 ⁢ π - δ , superscript subscript 𝑅 𝑚 𝑛 2 𝑧 cases Big-O superscript 𝑒 𝑧 𝑧 superscript 𝑧 𝑚 0 phase 𝑧 2 𝜋 Big-O superscript 𝑧 𝑚 3 2 𝜋 𝛿 phase 𝑧 0  and  2 𝜋 phase 𝑧 7 2 𝜋 𝛿 {\displaystyle{\displaystyle R_{m,n}^{(2)}(z)=\begin{cases}O\left(e^{-|z|+z}z^% {-m}\right),&0\leq\operatorname{ph}z\leq 2\pi,\\ O\left(z^{-m}\right),&-\frac{3}{2}\pi+\delta\leq\operatorname{ph}z\leq 0\text{% and }2\pi\leq\operatorname{ph}z\leq\frac{7}{2}\pi-\delta,\end{cases}}}
    0 references
    DLMF id
    DLMF:2.11.E23
    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.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2andec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2apdec
    0 references
    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1aadec
    0 references
    Q11141
    test
    R n ( j ) ⁢ ( z ) superscript subscript 𝑅 𝑛 𝑗 𝑧 {\displaystyle{\displaystyle R_{n}^{(j)}(z)}}
    xml-id
    C2.S11.XMD10.m1ddec
    0 references
    Q11144
    test
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C2.S11.XMD5.m1adec
    0 references
     
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