DLMF:7.9.E1 (Q2395): Difference between revisions

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Property / constraint
 

ℜ ⁡ z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}}

\realpart@@{z}>0
Property / constraint: ℜ ⁡ z > 0 𝑧 0 {\displaystyle{\displaystyle\Re z>0}} / 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
 
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: complementary error function / rank
 
Normal rank
Property / Symbols used: complementary error function / qualifier
 
Defining formula:

erfc ⁡ z complementary-error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}

\erfc@@{\NVar{z}}
Property / Symbols used: complementary error function / qualifier
 
xml-id: C7.S2.E2.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: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1adec
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.m1dec

Latest revision as of 01:47, 2 January 2020

No description defined
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English
DLMF:7.9.E1
No description defined

    Statements

    Defining formula
    π ⁢ e z 2 ⁢ erfc ⁡ z = z z 2 + 1 2 1 + 1 z 2 + 3 2 1 + 2 z 2 + ⋯ , 𝜋 superscript 𝑒 superscript 𝑧 2 complementary-error-function 𝑧 continued-fraction 𝑧 superscript 𝑧 2 continued-fraction 1 2 1 continued-fraction 1 superscript 𝑧 2 continued-fraction 3 2 1 continued-fraction 2 superscript 𝑧 2 ⋯ {\displaystyle{\displaystyle\sqrt{\pi}e^{z^{2}}\operatorname{erfc}z=\cfrac{z}{% z^{2}+\cfrac{\frac{1}{2}}{1+\cfrac{1}{z^{2}+\cfrac{\frac{3}{2}}{1+\cfrac{2}{z^% {2}+\cdots}}}}},}}
    0 references
    DLMF id
    DLMF:7.9.E1
    0 references
    constraint
    ℜ ⁡ z > 0 𝑧 0 {\displaystyle{\displaystyle\Re 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.m2adec
    0 references
    complementary error function
    Defining formula
    erfc ⁡ z complementary-error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}
    xml-id
    C7.S2.E2.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
    0 references
    Q11312
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1dec
    0 references
     
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