DLMF:16.2.E4 (Q5186): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
test:

( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

\Pochhammersym{\NVar{a}}{\NVar{n}}
Property / Symbols used: Q10759 / qualifier
 
xml-id: C5.S2.SS3.m1abdec
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.m5aadec
Property / Symbols used
 
Property / Symbols used: Q11690 / rank
 
Normal rank
Property / Symbols used: Q11690 / qualifier
 
test:

p 𝑝 {\displaystyle{\displaystyle p}}

p
Property / Symbols used: Q11690 / qualifier
 
xml-id: C16.S1.XMD1.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11691 / rank
 
Normal rank
Property / Symbols used: Q11691 / qualifier
 
test:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q11691 / qualifier
 
xml-id: C16.S1.XMD2.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11692 / rank
 
Normal rank
Property / Symbols used: Q11692 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11692 / qualifier
 
xml-id: C16.S1.XMD3.m1bdec

Latest revision as of 13:28, 2 January 2020

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English
DLMF:16.2.E4
No description defined

    Statements

    test
    ∑ k = 0 m ( 𝐚 ) k ( 𝐛 ) k ⁢ z k k ! = ( 𝐚 ) m ⁢ z m ( 𝐛 ) m ⁢ m ! ⁢ F p q + 2 ⁡ ( - m , 1 , 1 - m - 𝐛 1 - m - 𝐚 ; ( - 1 ) p + q + 1 z ) . superscript subscript 𝑘 0 𝑚 Pochhammer 𝐚 𝑘 Pochhammer 𝐛 𝑘 superscript 𝑧 𝑘 𝑘 Pochhammer 𝐚 𝑚 superscript 𝑧 𝑚 Pochhammer 𝐛 𝑚 𝑚 Gauss-hypergeometric-pFq 𝑞 2 𝑝 𝑚 1 1 𝑚 𝐛 1 𝑚 𝐚 superscript 1 𝑝 𝑞 1 𝑧 {\displaystyle{\displaystyle\sum_{k=0}^{m}\frac{{\left(\mathbf{a}\right)_{k}}}% {{\left(\mathbf{b}\right)_{k}}}\frac{z^{k}}{k!}=\frac{{\left(\mathbf{a}\right)% _{m}}z^{m}}{{\left(\mathbf{b}\right)_{m}}m!}{{}_{q+2}F_{p}}\left({-m,1,1-m-% \mathbf{b}\atop 1-m-\mathbf{a}};\frac{(-1)^{p+q+1}}{z}\right).}}
    0 references
    DLMF id
    DLMF:16.2.E4
    0 references
    Symbols used
    Q11125
    test
    F q p ⁡ ( a 1 , … , a p ; b 1 , … , b q ; z ) Gauss-hypergeometric-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}
    xml-id
    C16.S2.m1abdec
    0 references
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1abdec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    Q11690
    test
    p 𝑝 {\displaystyle{\displaystyle p}}
    xml-id
    C16.S1.XMD1.m1bdec
    0 references
    Q11691
    test
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C16.S1.XMD2.m1cdec
    0 references
    Q11692
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C16.S1.XMD3.m1bdec
    0 references
     
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