DLMF:18.7.E20 (Q5588): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
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.m1sdec

Latest revision as of 15:21, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:18.7.E20
No description defined

    Statements

    Defining formula
    H 2 ⁢ n + 1 ⁡ ( x ) = ( - 1 ) n ⁢ 2 2 ⁢ n + 1 ⁢ n ! ⁢ x ⁢ L n ( 1 2 ) ⁡ ( x 2 ) . Hermite-polynomial-H 2 𝑛 1 𝑥 superscript 1 𝑛 superscript 2 2 𝑛 1 𝑛 𝑥 Laguerre-polynomial-L 1 2 𝑛 superscript 𝑥 2 {\displaystyle{\displaystyle H_{2n+1}\left(x\right)=(-1)^{n}2^{2n+1}n!\,xL^{(% \frac{1}{2})}_{n}\left(x^{2}\right).}}
    0 references
    DLMF id
    DLMF:18.7.E20
    0 references
    Symbols used
    Q10922
    Defining formula
    H n ⁡ ( x ) Hermite-polynomial-H 𝑛 𝑥 {\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C18.S3.T1.t1.r13.m2acdec
    0 references
    Q11333
    Defining formula
    L n ( α ) ⁡ ( x ) Laguerre-polynomial-L 𝛼 𝑛 𝑥 {\displaystyle{\displaystyle L^{(\NVar{\alpha})}_{\NVar{n}}\left(\NVar{x}% \right)}}
    xml-id
    C18.S3.T1.t1.r12.m2aadec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1sdec
    0 references
    Q11727
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C18.S2.XMD3.m1sdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5588&oldid=57003"