DLMF:13.14.E18 (Q4507): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / constraint
 

μ ≠ 0 𝜇 0 {\displaystyle{\displaystyle\mu\not=0}}

\mu\not=0
Property / constraint: μ ≠ 0 𝜇 0 {\displaystyle{\displaystyle\mu\not=0}} / rank
 
Normal rank

Revision as of 17:48, 30 December 2019

No description defined
Language Label Description Also known as
English
DLMF:13.14.E18
No description defined

    Statements

    Defining formula
    W κ , μ ⁡ ( z ) = Γ ⁡ ( 2 ⁢ μ ) Γ ⁡ ( 1 2 + μ - κ ) ⁢ z 1 2 - μ + Γ ⁡ ( - 2 ⁢ μ ) Γ ⁡ ( 1 2 - μ - κ ) ⁢ z 1 2 + μ + O ⁡ ( z 3 2 - ℜ ⁡ μ ) , Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 Euler-Gamma 2 𝜇 Euler-Gamma 1 2 𝜇 𝜅 superscript 𝑧 1 2 𝜇 Euler-Gamma 2 𝜇 Euler-Gamma 1 2 𝜇 𝜅 superscript 𝑧 1 2 𝜇 Big-O superscript 𝑧 3 2 𝜇 {\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{\Gamma\left(2% \mu\right)}{\Gamma\left(\frac{1}{2}+\mu-\kappa\right)}z^{\frac{1}{2}-\mu}+% \frac{\Gamma\left(-2\mu\right)}{\Gamma\left(\frac{1}{2}-\mu-\kappa\right)}z^{% \frac{1}{2}+\mu}+O\left(z^{\frac{3}{2}-\Re\mu}\right),}}
    0 references
    DLMF id
    DLMF:13.14.E18
    0 references
    constraint
    0 ≤ ℜ ⁡ μ < 1 2 0 𝜇 1 2 {\displaystyle{\displaystyle 0\leq\Re\mu<\tfrac{1}{2}}}
    0 references
    0 ≤ ℜ ⁡ μ < 1 2 0 𝜇 1 2 {\displaystyle{\displaystyle 0\leq\Re\mu<\tfrac{1}{2}}}
    0 references
    μ ≠ 0 𝜇 0 {\displaystyle{\displaystyle\mu\not=0}}
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4507&oldid=18800"