DLMF:13.2.E16 (Q4306): Difference between revisions

From DRMF
Jump to navigation Jump to search
Changed an Item: Add constraint
Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q11557 / rank
 
Normal rank
Property / Symbols used: Q11557 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11557 / qualifier
 
xml-id: C13.S1.XMD6.m1odec

Latest revision as of 15:37, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:13.2.E16
No description defined

    Statements

    U ( a , b , z ) = Γ ( b - 1 ) Γ ( a ) z 1 - b + O ( z 2 - b ) , Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 Euler-Gamma 𝑏 1 Euler-Gamma 𝑎 superscript 𝑧 1 𝑏 Big-O superscript 𝑧 2 𝑏 {\displaystyle{\displaystyle U\left(a,b,z\right)=\frac{\Gamma\left(b-1\right)}% {\Gamma\left(a\right)}z^{1-b}+O\left(z^{2-\Re b}\right),}}
    0 references
    DLMF:13.2.E16
    0 references
    b 2 𝑏 2 {\displaystyle{\displaystyle\Re b\geq 2}}
    0 references
    b 2 𝑏 2 {\displaystyle{\displaystyle\Re b\geq 2}}
    0 references
    b 2 𝑏 2 {\displaystyle{\displaystyle b\not=2}}
    0 references
    O ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    C2.S1.E3.m2acdec
    0 references
    Γ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    C5.S2.E1.m2aedec
    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.m2aidec
    0 references
    absent {\displaystyle{\displaystyle\Re}}
    C1.S9.E2.m1adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C13.S1.XMD6.m1odec
    0 references