DLMF:13.2.E18 (Q4308): Difference between revisions

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‎Changed an Item: Add constraint
‎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.m2akdec

Revision as of 15:37, 2 January 2020

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DLMF:13.2.E18
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    Statements

    Defining formula
    U ⁡ ( a , b , z ) = Γ ⁡ ( b - 1 ) Γ ⁡ ( a ) ⁢ z 1 - b + Γ ⁡ ( 1 - b ) Γ ⁡ ( a - b + 1 ) + O ⁡ ( z 2 - ℜ ⁡ b ) , Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 Euler-Gamma 𝑏 1 Euler-Gamma 𝑎 superscript 𝑧 1 𝑏 Euler-Gamma 1 𝑏 Euler-Gamma 𝑎 𝑏 1 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}+\frac{\Gamma\left(1-b\right)}{\Gamma\left(a-b+1% \right)}+O\left(z^{2-\Re b}\right),}}
    0 references
    DLMF id
    DLMF:13.2.E18
    0 references
    constraint
    1 ≤ ℜ ⁡ b < 2 1 𝑏 2 {\displaystyle{\displaystyle 1\leq\Re b<2}}
    0 references
    1 ≤ ℜ ⁡ b < 2 1 𝑏 2 {\displaystyle{\displaystyle 1\leq\Re b<2}}
    0 references
    b ≠ 1 𝑏 1 {\displaystyle{\displaystyle b\not=1}}
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2aedec
    0 references
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2agdec
    0 references
    Kummer confluent hypergeometric function
    Defining formula
    U ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E6.m2akdec
    0 references
     
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