DLMF:13.3.E25 (Q4359): Difference between revisions

From DRMF
Jump to navigation Jump to search
Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Kummer confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: Kummer confluent hypergeometric function / qualifier
 
Defining formula:

U ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}

\KummerconfhyperU@{\NVar{a}}{\NVar{b}}{\NVar{z}}
Property / Symbols used: Kummer confluent hypergeometric function / qualifier
 
xml-id: C13.S2.E6.m2ajdec

Revision as of 15:44, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:13.3.E25
No description defined

    Statements

    d n d z n ( z b - 1 U ( a , b , z ) ) = ( - 1 ) n ( a - b + 1 ) n z b - n - 1 U ( a , b - n , z ) , derivative 𝑧 𝑛 superscript 𝑧 𝑏 1 Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 1 𝑛 Pochhammer 𝑎 𝑏 1 𝑛 superscript 𝑧 𝑏 𝑛 1 Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑛 𝑧 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{n}}{{\mathrm{d}z}^{n}}\left(z^% {b-1}U\left(a,b,z\right)\right)=(-1)^{n}{\left(a-b+1\right)_{n}}z^{b-n-1}U% \left(a,b-n,z\right),}}
    0 references
    DLMF:13.3.E25
    0 references
    U ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    C13.S2.E6.m2ajdec
    0 references