DLMF:13.4.E17 (Q4380): 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: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aldec

Revision as of 15:49, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:13.4.E17
No description defined

    Statements

    Defining formula
    U ⁡ ( a , b , z ) = z - a 2 ⁢ π ⁢ i ⁢ ∫ - i ⁢ ∞ i ⁢ ∞ Γ ⁡ ( a + t ) ⁢ Γ ⁡ ( 1 + a - b + t ) ⁢ Γ ⁡ ( - t ) Γ ⁡ ( a ) ⁢ Γ ⁡ ( 1 + a - b ) ⁢ z - t ⁢ d t , Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 superscript 𝑧 𝑎 2 𝜋 imaginary-unit superscript subscript imaginary-unit imaginary-unit Euler-Gamma 𝑎 𝑡 Euler-Gamma 1 𝑎 𝑏 𝑡 Euler-Gamma 𝑡 Euler-Gamma 𝑎 Euler-Gamma 1 𝑎 𝑏 superscript 𝑧 𝑡 𝑡 {\displaystyle{\displaystyle U\left(a,b,z\right)=\frac{z^{-a}}{2\pi\mathrm{i}}% \int_{-\mathrm{i}\infty}^{\mathrm{i}\infty}\frac{\Gamma\left(a+t\right)\Gamma% \left(1+a-b+t\right)\Gamma\left(-t\right)}{\Gamma\left(a\right)\Gamma\left(1+a% -b\right)}z^{-t}\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:13.4.E17
    0 references
    constraint
    | ph ⁡ z | < 3 2 ⁢ π phase 𝑧 3 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}{z}|<\tfrac{3}{2}\pi}}
    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
    Kummer confluent hypergeometric function
    Defining formula
    U ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E6.m2agdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aldec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4380&oldid=61233"