DLMF:13.2.E19 (Q4309): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2abdec

Revision as of 15:37, 2 January 2020

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DLMF:13.2.E19
No description defined

    Statements

    Defining formula
    U ⁡ ( a , 1 , z ) = - 1 Γ ⁡ ( a ) ⁢ ( ln ⁡ z + ψ ⁡ ( a ) + 2 ⁢ γ ) + O ⁡ ( z ⁢ ln ⁡ z ) , Kummer-confluent-hypergeometric-U 𝑎 1 𝑧 1 Euler-Gamma 𝑎 𝑧 digamma 𝑎 2 𝛾 Big-O 𝑧 𝑧 {\displaystyle{\displaystyle U\left(a,1,z\right)=-\frac{1}{\Gamma\left(a\right% )}\left(\ln z+\psi\left(a\right)+2\gamma\right)+O\left(z\ln z\right),}}
    0 references
    DLMF id
    DLMF:13.2.E19
    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.m2afdec
    0 references
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2ahdec
    0 references
    Euler’s constant
    Defining formula
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2adec
    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.m2aldec
    0 references
    psi (or digamma) function
    Defining formula
    ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E2.m2aadec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
    0 references
     
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