DLMF:15.10.E29 (Q5145)

From DRMF
Revision as of 14:19, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:15.10.E29
No description defined

    Statements

    Defining formula
    w 1 ⁢ ( z ) = e b ⁢ π ⁢ i ⁢ Γ ⁡ ( c ) ⁢ Γ ⁡ ( a - c + 1 ) Γ ⁡ ( a + b - c + 1 ) ⁢ Γ ⁡ ( c - b ) ⁢ w 3 ⁢ ( z ) + e ( b - c ) ⁢ π ⁢ i ⁢ Γ ⁡ ( c ) ⁢ Γ ⁡ ( a - c + 1 ) Γ ⁡ ( b ) ⁢ Γ ⁡ ( a - b + 1 ) ⁢ w 5 ⁢ ( z ) , subscript 𝑤 1 𝑧 superscript 𝑒 𝑏 𝜋 imaginary-unit Euler-Gamma 𝑐 Euler-Gamma 𝑎 𝑐 1 Euler-Gamma 𝑎 𝑏 𝑐 1 Euler-Gamma 𝑐 𝑏 subscript 𝑤 3 𝑧 superscript 𝑒 𝑏 𝑐 𝜋 imaginary-unit Euler-Gamma 𝑐 Euler-Gamma 𝑎 𝑐 1 Euler-Gamma 𝑏 Euler-Gamma 𝑎 𝑏 1 subscript 𝑤 5 𝑧 {\displaystyle{\displaystyle w_{1}(z)=e^{b\pi\mathrm{i}}\frac{\Gamma\left(c% \right)\Gamma\left(a-c+1\right)}{\Gamma\left(a+b-c+1\right)\Gamma\left(c-b% \right)}w_{3}(z)+e^{(b-c)\pi\mathrm{i}}\frac{\Gamma\left(c\right)\Gamma\left(a% -c+1\right)}{\Gamma\left(b\right)\Gamma\left(a-b+1\right)}w_{5}(z),}}
    0 references
    DLMF id
    DLMF:15.10.E29
    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.m2aldec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aidec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aidec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5145&oldid=45782"