DLMF:18.10.E7 (Q5631): 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: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

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

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2addec
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.m3afdec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1fdec
Property / Symbols used
 
Property / Symbols used: Q11727 / rank
 
Normal rank
Property / Symbols used: Q11727 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11727 / qualifier
 
xml-id: C18.S2.XMD3.m1adec

Latest revision as of 15:27, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:18.10.E7
No description defined

    Statements

    H n ( x ) = 2 n π 1 2 - ( x + i t ) n e - t 2 d t . Hermite-polynomial-H 𝑛 𝑥 superscript 2 𝑛 superscript 𝜋 1 2 superscript subscript superscript 𝑥 𝑖 𝑡 𝑛 superscript 𝑒 superscript 𝑡 2 𝑡 {\displaystyle{\displaystyle H_{n}\left(x\right)=\frac{2^{n}}{\pi^{\frac{1}{2}% }}\int_{-\infty}^{\infty}(x+it)^{n}e^{-t^{2}}\mathrm{d}t.}}
    0 references
    DLMF:18.10.E7
    0 references
    H n ( x ) Hermite-polynomial-H 𝑛 𝑥 {\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}
    C18.S3.T1.t1.r13.m2adec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2afdec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1afdec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2aadec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2addec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3afdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C18.S1.XMD6.m1fdec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C18.S2.XMD3.m1adec
    0 references