DLMF:7.9.E3 (Q2397): Difference between revisions

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‎Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q11312 / rank
 
Normal rank
Property / Symbols used: Q11312 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11312 / qualifier
 
xml-id: C7.S1.XMD2.m1bdec

Latest revision as of 01:47, 2 January 2020

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DLMF:7.9.E3
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    Statements

    Defining formula
    w ⁡ ( z ) = i π ⁢ 1 z - 1 2 z - 1 z - 3 2 z - 2 z - ⋯ , error-function-w 𝑧 𝑖 𝜋 continued-fraction 1 𝑧 continued-fraction 1 2 𝑧 continued-fraction 1 𝑧 continued-fraction 3 2 𝑧 continued-fraction 2 𝑧 ⋯ {\displaystyle{\displaystyle w\left(z\right)=\frac{i}{\sqrt{\pi}}\cfrac{1}{z-% \cfrac{\frac{1}{2}}{z-\cfrac{1}{z-\cfrac{\frac{3}{2}}{z-\cfrac{2}{z-\cdots}}}}% },}}
    0 references
    DLMF id
    DLMF:7.9.E3
    0 references
    constraint
    ℑ ⁡ z > 0 𝑧 0 {\displaystyle{\displaystyle\Im z>0}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    Faddeeva (or Faddeyeva) function
    Defining formula
    w ⁡ ( z ) error-function-w 𝑧 {\displaystyle{\displaystyle w\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E3.m2adec
    0 references
    Q10901
    Defining formula
    ℑ ⁡ absent {\displaystyle{\displaystyle\Im}}
    xml-id
    C1.S9.E2.m2adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q11312
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1bdec
    0 references
     
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