DLMF:13.14.E19 (Q4508): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: psi (or digamma) function / rank
 
Normal rank
Property / Symbols used: psi (or digamma) function / qualifier
 
Defining formula:

ψ ⁡ ( z ) digamma 𝑧 {\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}

\digamma@{\NVar{z}}
Property / Symbols used: psi (or digamma) function / qualifier
 
xml-id: C5.S2.E2.m2aadec

Revision as of 16:06, 2 January 2020

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DLMF:13.14.E19
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    Statements

    Defining formula
    W κ , 0 ⁡ ( z ) = - z Γ ⁡ ( 1 2 - κ ) ⁢ ( ln ⁡ z + ψ ⁡ ( 1 2 - κ ) + 2 ⁢ γ ) + O ⁡ ( z 3 / 2 ⁢ ln ⁡ z ) . Whittaker-confluent-hypergeometric-W 𝜅 0 𝑧 𝑧 Euler-Gamma 1 2 𝜅 𝑧 digamma 1 2 𝜅 2 𝛾 Big-O superscript 𝑧 3 2 𝑧 {\displaystyle{\displaystyle W_{\kappa,0}\left(z\right)=-\frac{\sqrt{z}}{% \Gamma\left(\frac{1}{2}-\kappa\right)}\left(\ln z+\psi\left(\tfrac{1}{2}-% \kappa\right)+2\gamma\right)+O\left(z^{\ifrac{3}{2}}\ln z\right).}}
    0 references
    DLMF id
    DLMF:13.14.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.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
    Euler’s constant
    Defining formula
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2adec
    0 references
    Whittaker confluent hypergeometric function
    Defining formula
    W κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E3.m2ajdec
    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
     
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