DLMF:12.5.E1 (Q4115): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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

Revision as of 15:08, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:12.5.E1
No description defined

    Statements

    Defining formula
    U ⁡ ( a , z ) = e - 1 4 ⁢ z 2 Γ ⁡ ( 1 2 + a ) ⁢ ∫ 0 ∞ t a - 1 2 ⁢ e - 1 2 ⁢ t 2 - z ⁢ t ⁢ d t , parabolic-U 𝑎 𝑧 superscript 𝑒 1 4 superscript 𝑧 2 Euler-Gamma 1 2 𝑎 superscript subscript 0 superscript 𝑡 𝑎 1 2 superscript 𝑒 1 2 superscript 𝑡 2 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle U\left(a,z\right)=\frac{e^{-\frac{1}{4}z^{2}}}{% \Gamma\left(\frac{1}{2}+a\right)}\int_{0}^{\infty}t^{a-\frac{1}{2}}e^{-\frac{1% }{2}t^{2}-zt}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:12.5.E1
    0 references
    constraint
    ℜ ⁡ a > - 1 2 𝑎 1 2 {\displaystyle{\displaystyle\Re a>-\tfrac{1}{2}}}
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4115&oldid=54657"