DLMF:15.10.E10 (Q5126): Difference between revisions

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imported>Admin
 
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Property / constraint
 

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ell=0,1,2,\dots,m}

\ell=0,1,2,\dots,m
Property / constraint: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ell=0,1,2,\dots,m} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / rank
 
Normal rank
Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / qualifier
 
test:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{z}}}

\hyperF@{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{z}}
Property / Symbols used: $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function / qualifier
 
xml-id: C15.S2.E1.m2aedec
Property / Symbols used
 
Property / Symbols used: Q10759 / rank
 
Normal rank
Property / Symbols used: Q10759 / qualifier
 
test:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Pochhammersym{\NVar{a}}{\NVar{n}}}

\Pochhammersym{\NVar{a}}{\NVar{n}}
Property / Symbols used: Q10759 / qualifier
 
xml-id: C5.S2.SS3.m1abdec
Property / Symbols used
 
Property / Symbols used: psi (or digamma) function / rank
 
Normal rank
Property / Symbols used: psi (or digamma) function / qualifier
 
test:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{\NVar{z}}}

\digamma@{\NVar{z}}
Property / Symbols used: psi (or digamma) function / qualifier
 
xml-id: C5.S2.E2.m2abdec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle !}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5abdec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
test:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11650 / rank
 
Normal rank
Property / Symbols used: Q11650 / qualifier
 
test:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n}

n
Property / Symbols used: Q11650 / qualifier
 
xml-id: C15.S1.XMD10.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11644 / rank
 
Normal rank
Property / Symbols used: Q11644 / qualifier
 
test:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z}

z
Property / Symbols used: Q11644 / qualifier
 
xml-id: C15.S1.XMD3.m1idec
Property / Symbols used
 
Property / Symbols used: Q11645 / rank
 
Normal rank
Property / Symbols used: Q11645 / qualifier
 
test:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a}

a
Property / Symbols used: Q11645 / qualifier
 
xml-id: C15.S1.XMD4.m1idec
Property / Symbols used
 
Property / Symbols used: Q11646 / rank
 
Normal rank
Property / Symbols used: Q11646 / qualifier
 
test:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b}

b
Property / Symbols used: Q11646 / qualifier
 
xml-id: C15.S1.XMD5.m1idec
Property / Symbols used
 
Property / Symbols used: Q11658 / rank
 
Normal rank
Property / Symbols used: Q11658 / qualifier
 
test:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k}

k
Property / Symbols used: Q11658 / qualifier
 
xml-id: C15.S1.XMD7.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11652 / rank
 
Normal rank
Property / Symbols used: Q11652 / qualifier
 
test:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ell}

\ell
Property / Symbols used: Q11652 / qualifier
 
xml-id: C15.S1.XMD8.m1dec
Property / Symbols used
 
Property / Symbols used: Q11651 / rank
 
Normal rank
Property / Symbols used: Q11651 / qualifier
 
test:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m}

m
Property / Symbols used: Q11651 / qualifier
 
xml-id: C15.S1.XMD9.m1bdec

Latest revision as of 13:14, 2 January 2020

No description defined
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English
DLMF:15.10.E10
No description defined

    Statements

    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@@{-m}{-\ell}{n}{z}\ln@@{z}-\sum_{k=1}^{n-1}\frac{(n-1)!(k-1)!}{(n-k-1)!\Pochhammersym{m+1}{k}\Pochhammersym{\ell+1}{k}}(-z)^{-k}+\sum_{k=0}^{\ell}\frac{\Pochhammersym{-m}{k}\Pochhammersym{-\ell}{k}}{\Pochhammersym{n}{k}k!}z^{k}\left(\digamma@{1+m-k}+\digamma@{1+\ell-k}-\digamma@{1+k}-\digamma@{n+k}\right)+(-1)^{\ell}\ell\,!\sum_{k=\ell+1}^{m}\frac{(k-1-\ell)!\Pochhammersym{-m}{k}}{\Pochhammersym{n}{k}k!}z^{k},}
    0 references
    DLMF id
    DLMF:15.10.E10
    0 references
    constraint
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ell=0,1,2,\dots,m}
    0 references
    Symbols used
    $$={{}_{2}F_{1}}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z}\right)$$ Gauss’ hypergeometric function
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \hyperF@{\NVar{a}}{\NVar{b}}{\NVar{c}}{\NVar{z}}}
    xml-id
    C15.S2.E1.m2aedec
    0 references
    Q10759
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Pochhammersym{\NVar{a}}{\NVar{n}}}
    xml-id
    C5.S2.SS3.m1abdec
    0 references
    psi (or digamma) function
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \digamma@{\NVar{z}}}
    xml-id
    C5.S2.E2.m2abdec
    0 references
    Q10755
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle !}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
    0 references
    principal branch of logarithm function
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
    0 references
    Q11650
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n}
    xml-id
    C15.S1.XMD10.m1bdec
    0 references
    Q11644
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z}
    xml-id
    C15.S1.XMD3.m1idec
    0 references
    Q11645
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a}
    xml-id
    C15.S1.XMD4.m1idec
    0 references
    Q11646
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b}
    xml-id
    C15.S1.XMD5.m1idec
    0 references
    Q11658
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k}
    xml-id
    C15.S1.XMD7.m1bdec
    0 references
    Q11652
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ell}
    xml-id
    C15.S1.XMD8.m1dec
    0 references
    Q11651
    test
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m}
    xml-id
    C15.S1.XMD9.m1bdec
    0 references
     
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