DLMF:13.14.E16 (Q4505): 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 / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1adec

Revision as of 16:06, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:13.14.E16
No description defined

    Statements

    Defining formula
    W κ , μ ⁡ ( z ) = 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 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}+O% \left(z^{\frac{3}{2}-\Re\mu}\right),}}
    0 references
    DLMF id
    DLMF:13.14.E16
    0 references
    constraint
    ℜ ⁡ μ ≥ 1 2 𝜇 1 2 {\displaystyle{\displaystyle\Re\mu\geq\frac{1}{2}}}
    0 references
    ℜ ⁡ μ ≥ 1 2 𝜇 1 2 {\displaystyle{\displaystyle\Re\mu\geq\frac{1}{2}}}
    0 references
    μ ≠ 1 2 𝜇 1 2 {\displaystyle{\displaystyle\mu\not=\frac{1}{2}}}
    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.m2abdec
    0 references
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2addec
    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.m2agdec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4505&oldid=62600"