DLMF:18.7.E23 (Q5591): Difference between revisions

From DRMF
Jump to navigation Jump to search
Newer edit →
‎Created a new Item: Wikidata Toolkit example test item creation
 
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10922 / rank
 
Normal rank
Property / Symbols used: Q10922 / qualifier
 
Defining formula:

H n ⁡ ( x ) Hermite-polynomial-H 𝑛 𝑥 {\displaystyle{\displaystyle H_{\NVar{n}}\left(\NVar{x}\right)}}

\HermitepolyH{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q10922 / qualifier
 
xml-id: C18.S3.T1.t1.r13.m2addec

Revision as of 15:21, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:18.7.E23
No description defined

    Statements

    Defining formula
    lim α → ∞ ⁡ α - 1 2 ⁢ n ⁢ P n ( α , α ) ⁡ ( α - 1 2 ⁢ x ) = H n ⁡ ( x ) 2 n ⁢ n ! . subscript → 𝛼 superscript 𝛼 1 2 𝑛 Jacobi-polynomial-P 𝛼 𝛼 𝑛 superscript 𝛼 1 2 𝑥 Hermite-polynomial-H 𝑛 𝑥 superscript 2 𝑛 𝑛 {\displaystyle{\displaystyle\lim_{\alpha\to\infty}\alpha^{-\frac{1}{2}n}P^{(% \alpha,\alpha)}_{n}\left(\alpha^{-\frac{1}{2}}x\right)=\frac{H_{n}\left(x% \right)}{2^{n}n!}.}}
    0 references
    DLMF id
    DLMF:18.7.E23
    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.m2addec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5591&oldid=57057"