DLMF:8.19.E17 (Q2703): Difference between revisions

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Property / constraint
 

| ph ⁡ z | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\pi}}

|\phase@@{z}|<\pi
Property / constraint: | ph ⁡ z | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\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.m2abdec
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: generalized exponential integral / rank
 
Normal rank
Property / Symbols used: generalized exponential integral / qualifier
 
test:

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

\genexpintE{\NVar{p}}@{\NVar{z}}
Property / Symbols used: generalized exponential integral / qualifier
 
xml-id: C8.S19.E1.m2audec
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.m1abdec
Property / Symbols used
 
Property / Symbols used: Q11323 / rank
 
Normal rank
Property / Symbols used: Q11323 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11323 / qualifier
 
xml-id: C8.S1.XMD2.m1odec
Property / Symbols used
 
Property / Symbols used: Q11377 / rank
 
Normal rank
Property / Symbols used: Q11377 / qualifier
 
test:

p 𝑝 {\displaystyle{\displaystyle p}}

p
Property / Symbols used: Q11377 / qualifier
 
xml-id: C8.S1.XMD4.m1mdec

Latest revision as of 13:11, 2 January 2020

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DLMF:8.19.E17
No description defined

    Statements

    test
    E p ⁡ ( z ) = e - z ⁢ ( 1 z + p 1 + 1 z + p + 1 1 + 2 z + ⋯ ) , exponential-integral-En 𝑝 𝑧 superscript 𝑒 𝑧 continued-fraction 1 𝑧 continued-fraction 𝑝 1 continued-fraction 1 𝑧 continued-fraction 𝑝 1 1 continued-fraction 2 𝑧 ⋯ {\displaystyle{\displaystyle E_{p}\left(z\right)=e^{-z}\left(\cfrac{1}{z+% \cfrac{p}{1+\cfrac{1}{z+\cfrac{p+1}{1+\cfrac{2}{z+\cdots}}}}}\right),}}
    0 references
    DLMF id
    DLMF:8.19.E17
    0 references
    constraint
    | ph ⁡ z | < π phase 𝑧 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\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.m2abdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2akdec
    0 references
    generalized exponential integral
    test
    E p ⁡ ( z ) exponential-integral-En 𝑝 𝑧 {\displaystyle{\displaystyle E_{\NVar{p}}\left(\NVar{z}\right)}}
    xml-id
    C8.S19.E1.m2audec
    0 references
    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1abdec
    0 references
    Q11323
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1odec
    0 references
    Q11377
    test
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C8.S1.XMD4.m1mdec
    0 references
     
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