DLMF:15.10.E18 (Q5134): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11647 / rank
 
Normal rank
Property / Symbols used: Q11647 / qualifier
 
Defining formula:

c 𝑐 {\displaystyle{\displaystyle c}}

c
Property / Symbols used: Q11647 / qualifier
 
xml-id: C15.S1.XMD6.m1ndec
Property / Symbols used
 
Property / Symbols used: Q11667 / rank
 
Normal rank
Property / Symbols used: Q11667 / qualifier
 
Defining formula:

w m ⁢ ( z ) subscript 𝑤 𝑚 𝑧 {\displaystyle{\displaystyle w_{m}(z)}}

w_{m}(z)
Property / Symbols used: Q11667 / qualifier
 
xml-id: C15.S10.XMD2.m1gdec

Latest revision as of 14:16, 2 January 2020

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DLMF:15.10.E18
No description defined

    Statements

    Defining formula
    w 4 ⁢ ( z ) = Γ ⁡ ( 1 - c ) ⁢ Γ ⁡ ( c - a - b + 1 ) Γ ⁡ ( 1 - a ) ⁢ Γ ⁡ ( 1 - b ) ⁢ w 1 ⁢ ( z ) + Γ ⁡ ( c - 1 ) ⁢ Γ ⁡ ( c - a - b + 1 ) Γ ⁡ ( c - a ) ⁢ Γ ⁡ ( c - b ) ⁢ w 2 ⁢ ( z ) , subscript 𝑤 4 𝑧 Euler-Gamma 1 𝑐 Euler-Gamma 𝑐 𝑎 𝑏 1 Euler-Gamma 1 𝑎 Euler-Gamma 1 𝑏 subscript 𝑤 1 𝑧 Euler-Gamma 𝑐 1 Euler-Gamma 𝑐 𝑎 𝑏 1 Euler-Gamma 𝑐 𝑎 Euler-Gamma 𝑐 𝑏 subscript 𝑤 2 𝑧 {\displaystyle{\displaystyle w_{4}(z)=\frac{\Gamma\left(1-c\right)\Gamma\left(% c-a-b+1\right)}{\Gamma\left(1-a\right)\Gamma\left(1-b\right)}w_{1}(z)+\frac{% \Gamma\left(c-1\right)\Gamma\left(c-a-b+1\right)}{\Gamma\left(c-a\right)\Gamma% \left(c-b\right)}w_{2}(z),}}
    0 references
    DLMF id
    DLMF:15.10.E18
    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.m2aadec
    0 references
    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1qdec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1qdec
    0 references
    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1qdec
    0 references
    Q11647
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1ndec
    0 references
    Q11667
    Defining formula
    w m ⁢ ( z ) subscript 𝑤 𝑚 𝑧 {\displaystyle{\displaystyle w_{m}(z)}}
    xml-id
    C15.S10.XMD2.m1gdec
    0 references
     
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