DLMF:8.6.E2 (Q2516): Difference between revisions

From DRMF
Jump to navigation Jump to search
Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3aadec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1adec
Property / Symbols used
 
Property / Symbols used: Q11323 / rank
 
Normal rank
Property / Symbols used: Q11323 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11323 / qualifier
 
xml-id: C8.S1.XMD2.m1adec
Property / Symbols used
 
Property / Symbols used: Q11324 / rank
 
Normal rank
Property / Symbols used: Q11324 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11324 / qualifier
 
xml-id: C8.S1.XMD3.m1adec

Latest revision as of 13:42, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:8.6.E2
No description defined

    Statements

    γ ( a , z ) = z 1 2 a 0 e - t t 1 2 a - 1 J a ( 2 z t ) d t , incomplete-gamma 𝑎 𝑧 superscript 𝑧 1 2 𝑎 superscript subscript 0 superscript 𝑒 𝑡 superscript 𝑡 1 2 𝑎 1 Bessel-J 𝑎 2 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle\gamma\left(a,z\right)=z^{\frac{1}{2}a}\int_{0}^{% \infty}e^{-t}t^{\frac{1}{2}a-1}J_{a}\left(2\sqrt{zt}\right)\mathrm{d}t,}}
    0 references
    DLMF:8.6.E2
    0 references
    a > 0 𝑎 0 {\displaystyle{\displaystyle\Re a>0}}
    0 references
    J ν ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    C10.S2.E2.m2adec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1aadec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2aadec
    0 references
    γ ( a , z ) incomplete-gamma 𝑎 𝑧 {\displaystyle{\displaystyle\gamma\left(\NVar{a},\NVar{z}\right)}}
    C8.S2.E1.m2aadec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3aadec
    0 references
    absent {\displaystyle{\displaystyle\Re}}
    C1.S9.E2.m1adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C8.S1.XMD2.m1adec
    0 references
    a 𝑎 {\displaystyle{\displaystyle a}}
    C8.S1.XMD3.m1adec
    0 references