DLMF:13.16.E12 (Q4563): Difference between revisions

From DRMF
Jump to navigation Jump to search
Newer edit →
‎Created a new Item: Wikidata Toolkit example test item creation
 
‎Changed an Item: Add constraint
Property / constraint
 

| ph ⁡ z | < 1 2 ⁢ π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}{z}|<\tfrac{1}{2}\pi}}

|\phase{z}|<\tfrac{1}{2}\pi
Property / constraint: | ph ⁡ z | < 1 2 ⁢ π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}{z}|<\tfrac{1}{2}\pi}} / rank
 
Normal rank

Revision as of 17:49, 30 December 2019

No description defined
Language Label Description Also known as
English
DLMF:13.16.E12
No description defined

    Statements

    Defining formula
    W κ , μ ⁡ ( z ) = e 1 2 ⁢ z 2 ⁢ π ⁢ i ⁢ ∫ - i ⁢ ∞ i ⁢ ∞ Γ ⁡ ( 1 2 + μ + t ) ⁢ Γ ⁡ ( 1 2 - μ + t ) Γ ⁡ ( 1 - κ + t ) ⁢ z - t ⁢ d t , Whittaker-confluent-hypergeometric-W 𝜅 𝜇 𝑧 superscript 𝑒 1 2 𝑧 2 𝜋 imaginary-unit superscript subscript imaginary-unit imaginary-unit Euler-Gamma 1 2 𝜇 𝑡 Euler-Gamma 1 2 𝜇 𝑡 Euler-Gamma 1 𝜅 𝑡 superscript 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle W_{\kappa,\mu}\left(z\right)=\frac{e^{\frac{1}{2}% z}}{2\pi\mathrm{i}}\int_{-\mathrm{i}\infty}^{\mathrm{i}\infty}\frac{\Gamma% \left(\frac{1}{2}+\mu+t\right)\Gamma\left(\frac{1}{2}-\mu+t\right)}{\Gamma% \left(1-\kappa+t\right)}z^{-t}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:13.16.E12
    0 references
    constraint
    | ph ⁡ z | < 1 2 ⁢ π phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}{z}|<\tfrac{1}{2}\pi}}
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4563&oldid=18823"