DLMF:8.6.E8 (Q2522): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older edit
imported>Admin
imported>Admin
 
(10 intermediate revisions by the same user not shown)
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: 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.m1agdec
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.m2agdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2adec
Property / Symbols used
 
Property / Symbols used: incomplete gamma function / rank
 
Normal rank
Property / Symbols used: incomplete gamma function / qualifier
 
test:

γ ⁡ ( a , z ) incomplete-gamma 𝑎 𝑧 {\displaystyle{\displaystyle\gamma\left(\NVar{a},\NVar{z}\right)}}

\incgamma@{\NVar{a}}{\NVar{z}}
Property / Symbols used: incomplete gamma function / qualifier
 
xml-id: C8.S2.E1.m2acdec
Property / Symbols used
 
Property / Symbols used: Q10818 / rank
 
Normal rank
Property / Symbols used: Q10818 / qualifier
 
test:

ℤ {\displaystyle{\displaystyle\mathbb{Z}}}

\Integers
Property / Symbols used: Q10818 / qualifier
 
xml-id: introduction.Sx4.p2.t1.r20.m2aadec
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.m3agdec
Property / Symbols used
 
Property / Symbols used: Q11245 / rank
 
Normal rank
Property / Symbols used: Q11245 / qualifier
 
test:

∉ {\displaystyle{\displaystyle\notin}}

\notin
Property / Symbols used: Q11245 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r11.m2aadec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
test:

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2aadec
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.m1gdec
Property / Symbols used
 
Property / Symbols used: Q11324 / rank
 
Normal rank
Property / Symbols used: Q11324 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11324 / qualifier
 
xml-id: C8.S1.XMD3.m1gdec

Latest revision as of 12:43, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:8.6.E8
No description defined

    Statements

    test
    γ ⁡ ( a , z ) = - i ⁢ z a 2 ⁢ sin ⁡ ( π ⁢ a ) ⁢ ∫ - 1 ( 0 + ) t a - 1 ⁢ e z ⁢ t ⁢ d t , incomplete-gamma 𝑎 𝑧 imaginary-unit superscript 𝑧 𝑎 2 𝜋 𝑎 superscript subscript 1 limit-from 0 superscript 𝑡 𝑎 1 superscript 𝑒 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle\gamma\left(a,z\right)=\frac{-\mathrm{i}z^{a}}{2% \sin\left(\pi a\right)}\int_{-1}^{(0+)}t^{a-1}e^{zt}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:8.6.E8
    0 references
    constraint
    a ∉ ℤ 𝑎 {\displaystyle{\displaystyle a\notin\mathbb{Z}}}
    0 references
    z ≠ 0 𝑧 0 {\displaystyle{\displaystyle z\neq 0}}
    0 references
    a ∉ ℤ 𝑎 ℤ {\displaystyle{\displaystyle a\notin\mathbb{Z}}}
    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
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1agdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2agdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    incomplete gamma function
    test
    γ ⁡ ( a , z ) incomplete-gamma 𝑎 𝑧 {\displaystyle{\displaystyle\gamma\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E1.m2acdec
    0 references
    Q10818
    test
    ℤ {\displaystyle{\displaystyle\mathbb{Z}}}
    xml-id
    introduction.Sx4.p2.t1.r20.m2aadec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3agdec
    0 references
    Q11245
    test
    ∉ {\displaystyle{\displaystyle\notin}}
    xml-id
    introduction.Sx4.p1.t1.r11.m2aadec
    0 references
    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
    0 references
    Q11323
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1gdec
    0 references
    Q11324
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1gdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q2522&oldid=12638"