DLMF:13.14.E33 (Q4525): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
(4 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Whittaker confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
Defining formula:

M κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}

\WhittakerconfhyperM{\NVar{\kappa}}{\NVar{\mu}}@{\NVar{z}}
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
xml-id: C13.S14.E2.m2apdec
Property / Symbols used
 
Property / Symbols used: Q11557 / rank
 
Normal rank
Property / Symbols used: Q11557 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11557 / qualifier
 
xml-id: C13.S1.XMD6.m1afdec
Property / Symbols used
 
Property / Symbols used: Whittaker confluent hypergeometric function / rank
 
Normal rank
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
Defining formula:

W κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}

\WhittakerconfhyperW{\NVar{\kappa}}{\NVar{\mu}}@{\NVar{z}}
Property / Symbols used: Whittaker confluent hypergeometric function / qualifier
 
xml-id: C13.S14.E3.m2audec

Latest revision as of 16:08, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:13.14.E33
No description defined

    Statements

    Defining formula
    W κ , μ ⁡ ( z ) = Γ ⁡ ( - 2 ⁢ μ ) Γ ⁡ ( 1 2 - μ - κ ) ⁢ M κ , μ ⁡ ( z ) + Γ ⁡ ( 2 ⁢ μ ) Γ ⁡ ( 1 2 + μ - κ ) ⁢ M κ , - μ ⁡ ( z ) . Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 Euler-Gamma 2 𝜇 Euler-Gamma 1 2 𝜇 𝜅 Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 Euler-Gamma 2 𝜇 Euler-Gamma 1 2 𝜇 𝜅 Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{\Gamma\left(-2% \mu\right)}{\Gamma\left(\frac{1}{2}-\mu-\kappa\right)}M_{\kappa,\mu}\left(z% \right)+\frac{\Gamma\left(2\mu\right)}{\Gamma\left(\frac{1}{2}+\mu-\kappa% \right)}M_{\kappa,-\mu}\left(z\right).}}
    0 references
    DLMF id
    DLMF:13.14.E33
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2andec
    0 references
    Whittaker confluent hypergeometric function
    Defining formula
    M κ , μ ⁡ ( z ) Whittaker-confluent-hypergeometric-M 𝜅 𝜇 𝑧 {\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
    xml-id
    C13.S14.E2.m2apdec
    0 references
    Q11557
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C13.S1.XMD6.m1afdec
    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.m2audec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4525&oldid=62708"