DLMF:15.10.E19 (Q5135): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11667 / rank
 
Normal rank
Property / Symbols used: Q11667 / qualifier
 
test:

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.m1hdec

Latest revision as of 13:16, 2 January 2020

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English
DLMF:15.10.E19
No description defined

    Statements

    test
    w 5 ⁢ ( z ) = Γ ⁡ ( 1 - c ) ⁢ Γ ⁡ ( a - b + 1 ) Γ ⁡ ( a - c + 1 ) ⁢ Γ ⁡ ( 1 - b ) ⁢ w 1 ⁢ ( z ) + e ( c - 1 ) ⁢ π ⁢ i ⁢ Γ ⁡ ( c - 1 ) ⁢ Γ ⁡ ( a - b + 1 ) Γ ⁡ ( a ) ⁢ Γ ⁡ ( c - b ) ⁢ w 2 ⁢ ( z ) , subscript 𝑤 5 𝑧 Euler-Gamma 1 𝑐 Euler-Gamma 𝑎 𝑏 1 Euler-Gamma 𝑎 𝑐 1 Euler-Gamma 1 𝑏 subscript 𝑤 1 𝑧 superscript 𝑒 𝑐 1 𝜋 imaginary-unit Euler-Gamma 𝑐 1 Euler-Gamma 𝑎 𝑏 1 Euler-Gamma 𝑎 Euler-Gamma 𝑐 𝑏 subscript 𝑤 2 𝑧 {\displaystyle{\displaystyle w_{5}(z)=\frac{\Gamma\left(1-c\right)\Gamma\left(% a-b+1\right)}{\Gamma\left(a-c+1\right)\Gamma\left(1-b\right)}w_{1}(z)+e^{(c-1)% \pi\mathrm{i}}\frac{\Gamma\left(c-1\right)\Gamma\left(a-b+1\right)}{\Gamma% \left(a\right)\Gamma\left(c-b\right)}w_{2}(z),}}
    0 references
    DLMF id
    DLMF:15.10.E19
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2abdec
    0 references
    Q11644
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1rdec
    0 references
    Q11645
    test
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1rdec
    0 references
    Q11646
    test
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1rdec
    0 references
    Q11647
    test
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1odec
    0 references
    Q11667
    test
    w m ⁢ ( z ) subscript 𝑤 𝑚 𝑧 {\displaystyle{\displaystyle w_{m}(z)}}
    xml-id
    C15.S10.XMD2.m1hdec
    0 references
     
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