DLMF:33.6.E4 (Q9536): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11581 / rank
 
Normal rank
Property / Symbols used: Q11581 / qualifier
 
test:

F 1 2 ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F-as-2F1 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}

\genhyperF{2}{1}@{\NVar{a},\NVar{b}}{\NVar{c}}{\NVar{z}}
Property / Symbols used: Q11581 / qualifier
 
xml-id: C16.S2.m5adec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5adec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

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

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q12669 / rank
 
Normal rank
Property / Symbols used: Q12669 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12669 / qualifier
 
xml-id: C33.S1.XMD1.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12666 / rank
 
Normal rank
Property / Symbols used: Q12666 / qualifier
 
test:

ℓ ℓ {\displaystyle{\displaystyle\ell}}

\ell
Property / Symbols used: Q12666 / qualifier
 
xml-id: C33.S1.XMD2.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12668 / rank
 
Normal rank
Property / Symbols used: Q12668 / qualifier
 
test:

η 𝜂 {\displaystyle{\displaystyle\eta}}

\eta
Property / Symbols used: Q12668 / qualifier
 
xml-id: C33.S1.XMD7.m1cdec

Latest revision as of 13:23, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:33.6.E4
No description defined

    Statements

    test
    A k ℓ ⁢ ( η ) = ( - i ) k - ℓ - 1 ( k - ℓ - 1 ) ! ⁢ F 1 2 ⁡ ( ℓ + 1 - k , ℓ + 1 - i ⁢ η ; 2 ⁢ ℓ + 2 ; 2 ) . superscript subscript 𝐴 𝑘 ℓ 𝜂 superscript imaginary-unit 𝑘 ℓ 1 𝑘 ℓ 1 Gauss-hypergeometric-F-as-2F1 ℓ 1 𝑘 ℓ 1 imaginary-unit 𝜂 2 ℓ 2 2 {\displaystyle{\displaystyle A_{k}^{\ell}(\eta)=\dfrac{(-\mathrm{i})^{k-\ell-1% }}{(k-\ell-1)!}\*{{}_{2}F_{1}}\left(\ell+1-k,\ell+1-\mathrm{i}\eta;2\ell+2;2% \right).}}
    0 references
    DLMF id
    DLMF:33.6.E4
    0 references
    Symbols used
    Q11581
    test
    F 1 2 ⁡ ( a , b ; c ; z ) Gauss-hypergeometric-F-as-2F1 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle{{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};% \NVar{z}\right)}}
    xml-id
    C16.S2.m5adec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q12669
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C33.S1.XMD1.m1cdec
    0 references
    Q12666
    test
    ℓ ℓ {\displaystyle{\displaystyle\ell}}
    xml-id
    C33.S1.XMD2.m1cdec
    0 references
    Q12668
    test
    η 𝜂 {\displaystyle{\displaystyle\eta}}
    xml-id
    C33.S1.XMD7.m1cdec
    0 references
     
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