DLMF:7.7.E1 (Q2371): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
 
imported>Admin
 
(7 intermediate revisions by the same user not shown)
Property / constraint
 

| ph z | 1 4 π phase 𝑧 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\frac{1}{4}\pi}}

|\phase@@{z}|\leq\frac{1}{4}\pi
Property / constraint: | ph z | 1 4 π phase 𝑧 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\frac{1}{4}\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.m2adec
Property / Symbols used
 
Property / Symbols used: complementary error function / rank
 
Normal rank
Property / Symbols used: complementary error function / qualifier
 
test:

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: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1adec
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.m2adec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3adec
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: Q11312 / rank
 
Normal rank
Property / Symbols used: Q11312 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11312 / qualifier
 
xml-id: C7.S1.XMD2.m1dec

Latest revision as of 00:43, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:7.7.E1
No description defined

    Statements

    erfc z = 2 π e - z 2 0 e - z 2 t 2 t 2 + 1 d t , complementary-error-function 𝑧 2 𝜋 superscript 𝑒 superscript 𝑧 2 superscript subscript 0 superscript 𝑒 superscript 𝑧 2 superscript 𝑡 2 superscript 𝑡 2 1 𝑡 {\displaystyle{\displaystyle\operatorname{erfc}z=\frac{2}{\pi}e^{-z^{2}}\int_{% 0}^{\infty}\frac{e^{-z^{2}t^{2}}}{t^{2}+1}\mathrm{d}t,}}
    0 references
    0 references
    | ph z | 1 4 π phase 𝑧 1 4 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\frac{1}{4}\pi}}
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
    0 references
    erfc z complementary-error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}
    C7.S2.E2.m2adec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1adec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2adec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3adec
    0 references
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    C1.S9.E7.m1adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C7.S1.XMD2.m1dec
    0 references