DLMF:15.10.E33 (Q5149): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2amdec

Revision as of 14:20, 2 January 2020

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DLMF:15.10.E33
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    Statements

    Defining formula
    w 1 ⁢ ( z ) = e ( c - a ) ⁢ π ⁢ i ⁢ Γ ⁡ ( c ) ⁢ Γ ⁡ ( 1 - b ) Γ ⁡ ( a ) ⁢ Γ ⁡ ( c - a - b + 1 ) ⁢ w 4 ⁢ ( z ) + e - a ⁢ π ⁢ i ⁢ Γ ⁡ ( c ) ⁢ Γ ⁡ ( 1 - b ) Γ ⁡ ( a - b + 1 ) ⁢ Γ ⁡ ( c - a ) ⁢ w 5 ⁢ ( z ) , subscript 𝑤 1 𝑧 superscript 𝑒 𝑐 𝑎 𝜋 imaginary-unit Euler-Gamma 𝑐 Euler-Gamma 1 𝑏 Euler-Gamma 𝑎 Euler-Gamma 𝑐 𝑎 𝑏 1 subscript 𝑤 4 𝑧 superscript 𝑒 𝑎 𝜋 imaginary-unit Euler-Gamma 𝑐 Euler-Gamma 1 𝑏 Euler-Gamma 𝑎 𝑏 1 Euler-Gamma 𝑐 𝑎 subscript 𝑤 5 𝑧 {\displaystyle{\displaystyle w_{1}(z)=e^{(c-a)\pi\mathrm{i}}\frac{\Gamma\left(% c\right)\Gamma\left(1-b\right)}{\Gamma\left(a\right)\Gamma\left(c-a-b+1\right)% }w_{4}(z)+e^{-a\pi\mathrm{i}}\frac{\Gamma\left(c\right)\Gamma\left(1-b\right)}% {\Gamma\left(a-b+1\right)\Gamma\left(c-a\right)}w_{5}(z),}}
    0 references
    DLMF id
    DLMF:15.10.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.m2apdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2amdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2amdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2amdec
    0 references
     
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