DLMF:15.2.E2 (Q4978): Difference between revisions

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Property / constraint
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| z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}

|z|<1
Property / constraint: | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}} / rank
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Normal rank
Property / Symbols used
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Property / Symbols used: gamma function / rank
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Normal rank
Property / Symbols used: gamma function / qualifier
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test:

Ξ“ ⁑ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
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xml-id: C5.S2.E1.m2aadec
Property / Symbols used
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Property / Symbols used: Q10759 / rank
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Normal rank
Property / Symbols used: Q10759 / qualifier
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test:

( a ) n Pochhammer π‘Ž 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}

\Pochhammersym{\NVar{a}}{\NVar{n}}
Property / Symbols used: Q10759 / qualifier
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xml-id: C5.S2.SS3.m1aadec
Property / Symbols used
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Property / Symbols used: Q10755 / rank
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Normal rank
Property / Symbols used: Q10755 / qualifier
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test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
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xml-id: introduction.Sx4.p1.t1.r15.m5aadec
Property / Symbols used
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Property / Symbols used: scaled (or Olver’s) generalized hypergeometric function / rank
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Normal rank
Property / Symbols used: scaled (or Olver’s) generalized hypergeometric function / qualifier
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test:

𝐅 q p ⁑ ( 𝐚 ; 𝐛 ; ) hypergeometric-bold-pFq 𝑝 π‘ž 𝐚 𝐛 {\displaystyle{\displaystyle{{}_{\NVar{p}}{\mathbf{F}}_{\NVar{q}}}\left(\NVar{% \mathbf{a}};\NVar{\mathbf{b}};\right)\)\@add@PDF@RDFa@triples\end{document}}}

\genhyperOlverF{\NVar{p}}{\NVar{q}}@{\NVar{\mathbf{a}}}{\NVar{\mathbf{b}}}{% \NVar{z}}
Property / Symbols used: scaled (or Olver’s) generalized hypergeometric function / qualifier
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xml-id: C16.S2.E5.m2adec
Property / Symbols used
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Property / Symbols used: Q11648 / rank
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Normal rank
Property / Symbols used: Q11648 / qualifier
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test:

s 𝑠 {\displaystyle{\displaystyle s}}

s
Property / Symbols used: Q11648 / qualifier
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xml-id: C15.S1.XMD11.m1adec
Property / Symbols used
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Property / Symbols used: Q11644 / rank
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Normal rank
Property / Symbols used: Q11644 / qualifier
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test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11644 / qualifier
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xml-id: C15.S1.XMD3.m1adec
Property / Symbols used
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Property / Symbols used: Q11645 / rank
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Normal rank
Property / Symbols used: Q11645 / qualifier
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test:

a π‘Ž {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11645 / qualifier
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xml-id: C15.S1.XMD4.m1adec
Property / Symbols used
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Property / Symbols used: Q11646 / rank
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Normal rank
Property / Symbols used: Q11646 / qualifier
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test:

b 𝑏 {\displaystyle{\displaystyle b}}

b
Property / Symbols used: Q11646 / qualifier
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xml-id: C15.S1.XMD5.m1adec
Property / Symbols used
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Property / Symbols used: Q11647 / rank
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Normal rank
Property / Symbols used: Q11647 / qualifier
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test:

c 𝑐 {\displaystyle{\displaystyle c}}

c
Property / Symbols used: Q11647 / qualifier
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xml-id: C15.S1.XMD6.m1adec

Latest revision as of 12:46, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:15.2.E2
No description defined

    Statements

    test
    𝐅 ⁑ ( a , b ; c ; z ) = βˆ‘ s = 0 ∞ ( a ) s ⁒ ( b ) s Ξ“ ⁑ ( c + s ) ⁒ s ! ⁒ z s , scaled-hypergeometric-bold-F π‘Ž 𝑏 𝑐 𝑧 superscript subscript 𝑠 0 Pochhammer π‘Ž 𝑠 Pochhammer 𝑏 𝑠 Euler-Gamma 𝑐 𝑠 𝑠 superscript 𝑧 𝑠 {\displaystyle{\displaystyle\mathbf{F}\left(a,b;c;z\right)=\sum_{s=0}^{\infty}% \frac{{\left(a\right)_{s}}{\left(b\right)_{s}}}{\Gamma\left(c+s\right)s!}z^{s}% ,}}
    0 references
    DLMF id
    DLMF:15.2.E2
    0 references
    constraint
    | z | < 1 𝑧 1 {\displaystyle{\displaystyle|z|<1}}
    0 references
    Symbols used
    gamma function
    test
    Ξ“ ⁑ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    Q10759
    test
    ( a ) n Pochhammer π‘Ž 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1aadec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    scaled (or Olver’s) generalized hypergeometric function
    test
    𝐅 q p ⁑ ( 𝐚 ; 𝐛 ; ) hypergeometric-bold-pFq 𝑝 π‘ž 𝐚 𝐛 {\displaystyle{\displaystyle{{}_{\NVar{p}}{\mathbf{F}}_{\NVar{q}}}\left(\NVar{% \mathbf{a}};\NVar{\mathbf{b}};\right)\)\@add@PDF@RDFa@triples\end{document}}}
    xml-id
    C16.S2.E5.m2adec
    0 references
    Q11648
    test
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C15.S1.XMD11.m1adec
    0 references
    Q11644
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C15.S1.XMD3.m1adec
    0 references
    Q11645
    test
    a π‘Ž {\displaystyle{\displaystyle a}}
    xml-id
    C15.S1.XMD4.m1adec
    0 references
    Q11646
    test
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C15.S1.XMD5.m1adec
    0 references
    Q11647
    test
    c 𝑐 {\displaystyle{\displaystyle c}}
    xml-id
    C15.S1.XMD6.m1adec
    0 references
     
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