DLMF:18.19.E7 (Q5837)

From DRMF
Revision as of 01:30, 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:18.19.E7
No description defined

    Statements

    Defining formula
    w ( λ ) ⁢ ( z ; ϕ ) = Γ ⁡ ( λ + i ⁢ z ) ⁢ Γ ⁡ ( λ - i ⁢ z ) ⁢ e ( 2 ⁢ ϕ - π ) ⁢ z , superscript 𝑤 𝜆 𝑧 italic-ϕ Euler-Gamma 𝜆 𝑖 𝑧 Euler-Gamma 𝜆 𝑖 𝑧 superscript 𝑒 2 italic-ϕ 𝜋 𝑧 {\displaystyle{\displaystyle w^{(\lambda)}(z;\phi)=\Gamma\left(\lambda+iz% \right)\Gamma\left(\lambda-iz\right)e^{(2\phi-\pi)z},}}
    0 references
    DLMF id
    DLMF:18.19.E7
    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.m2acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    Q11729
    Defining formula
    w ⁢ ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}}
    xml-id
    C18.S1.XMD10.m1bdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q5837&oldid=32061"