DLMF:15.10.E23 (Q5139): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2addec
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.m2addec
Property / Symbols used
 
Property / Symbols used: Q11644 / rank
 
Normal rank
Property / Symbols used: Q11644 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11644 / qualifier
 
xml-id: C15.S1.XMD3.m1vdec
Property / Symbols used
 
Property / Symbols used: Q11645 / rank
 
Normal rank
Property / Symbols used: Q11645 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11645 / qualifier
 
xml-id: C15.S1.XMD4.m1vdec
Property / Symbols used
 
Property / Symbols used: Q11646 / rank
 
Normal rank
Property / Symbols used: Q11646 / qualifier
 
Defining formula:

b 𝑏 {\displaystyle{\displaystyle b}}

b
Property / Symbols used: Q11646 / qualifier
 
xml-id: C15.S1.XMD5.m1vdec
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.m1sdec
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.m1ldec

Latest revision as of 14:17, 2 January 2020

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DLMF:15.10.E23
No description defined

    Statements

    Defining formula
    w 5 ⁢ ( z ) = e a ⁢ π ⁢ i ⁢ Γ ⁡ ( a - b + 1 ) ⁢ Γ ⁡ ( c - a - b ) Γ ⁡ ( 1 - b ) ⁢ Γ ⁡ ( c - b ) ⁢ w 3 ⁢ ( z ) + e ( c - b ) ⁢ π ⁢ i ⁢ Γ ⁡ ( a - b + 1 ) ⁢ Γ ⁡ ( a + b - c ) Γ ⁡ ( a ) ⁢ Γ ⁡ ( a - c + 1 ) ⁢ w 4 ⁢ ( z ) , subscript 𝑤 5 𝑧 superscript 𝑒 𝑎 𝜋 imaginary-unit Euler-Gamma 𝑎 𝑏 1 Euler-Gamma 𝑐 𝑎 𝑏 Euler-Gamma 1 𝑏 Euler-Gamma 𝑐 𝑏 subscript 𝑤 3 𝑧 superscript 𝑒 𝑐 𝑏 𝜋 imaginary-unit Euler-Gamma 𝑎 𝑏 1 Euler-Gamma 𝑎 𝑏 𝑐 Euler-Gamma 𝑎 Euler-Gamma 𝑎 𝑐 1 subscript 𝑤 4 𝑧 {\displaystyle{\displaystyle w_{5}(z)=e^{a\pi\mathrm{i}}\frac{\Gamma\left(a-b+% 1\right)\Gamma\left(c-a-b\right)}{\Gamma\left(1-b\right)\Gamma\left(c-b\right)% }w_{3}(z)+e^{(c-b)\pi\mathrm{i}}\frac{\Gamma\left(a-b+1\right)\Gamma\left(a+b-% c\right)}{\Gamma\left(a\right)\Gamma\left(a-c+1\right)}w_{4}(z),}}
    0 references
    DLMF id
    DLMF:15.10.E23
    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.m2afdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2addec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2addec
    0 references
    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1vdec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1vdec
    0 references
    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1vdec
    0 references
    Q11647
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1sdec
    0 references
    Q11667
    Defining formula
    w m ⁢ ( z ) subscript 𝑤 𝑚 𝑧 {\displaystyle{\displaystyle w_{m}(z)}}
    xml-id
    C15.S10.XMD2.m1ldec
    0 references
     
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