DLMF:15.15.E1 (Q5177): 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.m1dec

Latest revision as of 14:26, 2 January 2020

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DLMF:15.15.E1
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    Statements

    Defining formula
    𝐅 ⁡ ( a , b c ; 1 z ) = ( 1 - z 0 z ) - a ⁢ ∑ s = 0 ∞ ( a ) s s ! ⁢ 𝐅 ⁡ ( - s , b c ; 1 z 0 ) ⁢ ( 1 - z z 0 ) - s . scaled-hypergeometric-bold-F 𝑎 𝑏 𝑐 1 𝑧 superscript 1 subscript 𝑧 0 𝑧 𝑎 superscript subscript 𝑠 0 subscript 𝑎 𝑠 𝑠 scaled-hypergeometric-bold-F 𝑠 𝑏 𝑐 1 subscript 𝑧 0 superscript 1 𝑧 subscript 𝑧 0 𝑠 {\displaystyle{\displaystyle\mathbf{F}\left({a,b\atop c};\frac{1}{z}\right)=% \left(1-\frac{z_{0}}{z}\right)^{-a}\sum_{s=0}^{\infty}\frac{(a)_{s}}{s!}\*% \mathbf{F}\left({-s,b\atop c};\frac{1}{z_{0}}\right)\left(1-\frac{z}{z_{0}}% \right)^{-s}.}}
    0 references
    DLMF id
    DLMF:15.15.E1
    0 references
    Symbols used
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    $$={{}_{2}{\mathbf{F}}_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Olver’s hypergeometric function
    Defining formula
    𝐅 ⁡ ( a , b ; c ; z ) scaled-hypergeometric-bold-F 𝑎 𝑏 𝑐 𝑧 {\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z% }\right)}}
    xml-id
    C15.S2.E2.m2adec
    0 references
    Q11648
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C15.S1.XMD11.m1dec
    0 references
    Q11644
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1dec
    0 references
    Q11645
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1dec
    0 references
    Q11646
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1dec
    0 references
    Q11647
    Defining formula
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1dec
    0 references
     
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