DLMF:4.4.E16 (Q1550): Difference between revisions

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Property / constraint
 

| ph ⁡ z | ≤ 1 2 ⁢ π - δ phase 𝑧 1 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi-\delta}}

|\phase@@{z}|\leq\tfrac{1}{2}\pi-\delta
Property / constraint: | ph ⁡ z | ≤ 1 2 ⁢ π - δ phase 𝑧 1 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi-\delta}} / rank
 
Normal rank
Property / constraint
 

| ph ⁡ z | ≤ 1 2 ⁢ π - δ ph 𝑧 1 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi-\delta}}

|\operatorname{ph}z|\leq\tfrac{1}{2}\pi-\delta
Property / constraint: | ph ⁡ z | ≤ 1 2 ⁢ π - δ ph 𝑧 1 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi-\delta}} / rank
 
Normal rank
Property / constraint
 

< 1 2 ⁢ π absent 1 2 𝜋 {\displaystyle{\displaystyle<\tfrac{1}{2}\pi}}

<\tfrac{1}{2}\pi
Property / constraint: < 1 2 ⁢ π absent 1 2 𝜋 {\displaystyle{\displaystyle<\tfrac{1}{2}\pi}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2ajdec
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.m2ajdec
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.m1adec
Property / Symbols used
 
Property / Symbols used: Q11221 / rank
 
Normal rank
Property / Symbols used: Q11221 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11221 / qualifier
 
xml-id: C4.S1.XMD4.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11217 / rank
 
Normal rank
Property / Symbols used: Q11217 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11217 / qualifier
 
xml-id: C4.S1.XMD8.m1dec
Property / Symbols used
 
Property / Symbols used: Q11224 / rank
 
Normal rank
Property / Symbols used: Q11224 / qualifier
 
test:

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

\delta
Property / Symbols used: Q11224 / qualifier
 
xml-id: C4.S4.XMD1.m1dec

Latest revision as of 17:06, 1 January 2020

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DLMF:4.4.E16
No description defined

    Statements

    test
    lim z → ∞ ⁡ z a ⁢ e - z = 0 , subscript → 𝑧 superscript 𝑧 𝑎 superscript 𝑒 𝑧 0 {\displaystyle{\displaystyle\lim_{z\to\infty}z^{a}e^{-z}=0,}}
    0 references
    DLMF id
    DLMF:4.4.E16
    0 references
    comment
    Warning: Falling back to standard tex;
    0 references
    constraint
    | ph ⁡ z | ≤ 1 2 ⁢ π - δ phase 𝑧 1 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi-\delta}}
    0 references
    | ph ⁡ z | ≤ 1 2 ⁢ π - δ ph 𝑧 1 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi-\delta}}
    0 references
    < 1 2 ⁢ π absent 1 2 𝜋 {\displaystyle{\displaystyle<\tfrac{1}{2}\pi}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ajdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ajdec
    0 references
    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
    0 references
    Q11221
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C4.S1.XMD4.m1cdec
    0 references
    Q11217
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1dec
    0 references
    Q11224
    test
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    xml-id
    C4.S4.XMD1.m1dec
    0 references
     
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