DLMF:6.12.E1 (Q2289): Difference between revisions

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Property / constraint
 

| ph ⁡ z | ≤ 3 2 ⁢ π - δ ( < 3 2 ⁢ π ) ph 𝑧 annotated 3 2 𝜋 𝛿 absent 3 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{3}{2}\pi-\delta(<% \tfrac{3}{2}\pi)}}

|\operatorname{ph}z|\leq\tfrac{3}{2}\pi-\delta(<\tfrac{3}{2}\pi)
Property / constraint: | ph ⁡ z | ≤ 3 2 ⁢ π - δ ( < 3 2 ⁢ π ) ph 𝑧 annotated 3 2 𝜋 𝛿 absent 3 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{3}{2}\pi-\delta(<% \tfrac{3}{2}\pi)}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q10931 / rank
 
Normal rank
Property / Symbols used: Q10931 / qualifier
 
Defining formula:

∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}

\asympexp
Property / Symbols used: Q10931 / qualifier
 
xml-id: C2.S1.SS3.p1.m11adec
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
 
Defining formula:

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.m2adec
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2adec
Property / Symbols used
 
Property / Symbols used: exponential integral / rank
 
Normal rank
Property / Symbols used: exponential integral / qualifier
 
Defining formula:

E 1 ⁡ ( z ) exponential-integral 𝑧 {\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}

\expintE@{\NVar{z}}
Property / Symbols used: exponential integral / qualifier
 
xml-id: C6.S2.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5adec
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
Defining formula:

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

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1adec
Property / Symbols used
 
Property / Symbols used: Q11305 / rank
 
Normal rank
Property / Symbols used: Q11305 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11305 / qualifier
 
xml-id: C6.S1.XMD2.m1dec

Latest revision as of 01:31, 2 January 2020

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English
DLMF:6.12.E1
No description defined

    Statements

    Defining formula
    E 1 ⁡ ( z ) ∼ e - z z ⁢ ( 1 - 1 ! z + 2 ! z 2 - 3 ! z 3 + ⋯ ) , asymptotic-expansion exponential-integral 𝑧 superscript 𝑒 𝑧 𝑧 1 1 𝑧 2 superscript 𝑧 2 3 superscript 𝑧 3 ⋯ {\displaystyle{\displaystyle E_{1}\left(z\right)\sim\frac{e^{-z}}{z}\left(1-% \frac{1!}{z}+\frac{2!}{z^{2}}-\frac{3!}{z^{3}}+\cdots\right),}}
    0 references
    DLMF id
    DLMF:6.12.E1
    0 references
    constraint
    | ph ⁡ z | ≤ 3 2 ⁢ π - δ ( < 3 2 ⁢ π ) phase 𝑧 annotated 3 2 𝜋 𝛿 absent 3 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{3}{2}\pi-\delta(<% \tfrac{3}{2}\pi)}}
    0 references
    z → ∞ → 𝑧 {\displaystyle{\displaystyle z\to\infty}}
    0 references
    | ph ⁡ z | ≤ 3 2 ⁢ π - δ ( < 3 2 ⁢ π ) ph 𝑧 annotated 3 2 𝜋 𝛿 absent 3 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{3}{2}\pi-\delta(<% \tfrac{3}{2}\pi)}}
    0 references
    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    exponential integral
    Defining formula
    E 1 ⁡ ( z ) exponential-integral 𝑧 {\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E1.m2adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
    0 references
    Q11305
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C6.S1.XMD2.m1dec
    0 references
     
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