DLMF:18.28.E10 (Q5985): Difference between revisions

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‎Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q11298 / rank
 
Normal rank
Property / Symbols used: Q11298 / qualifier
 
Defining formula:

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

\qPochhammer{\NVar{a}}{\NVar{q}}{\NVar{n}}
Property / Symbols used: Q11298 / qualifier
 
xml-id: C17.S2.SS1.p1.m2agdec
Property / Symbols used
 
Property / Symbols used: $$q^{-1}$$ -Al-Salam–Chihara polynomial / rank
 
Normal rank
Property / Symbols used: $$q^{-1}$$ -Al-Salam–Chihara polynomial / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qinvAlSalamChiharapolyQ{\NVar{n}}@{\NVar{x}}{\NVar{a}}{\NVar{b}}{\NVar{q}^{-1}}}

\qinvAlSalamChiharapolyQ{\NVar{n}}@{\NVar{x}}{\NVar{a}}{\NVar{b}}{\NVar{q}^{-1}}
Property / Symbols used: $$q^{-1}$$ -Al-Salam–Chihara polynomial / qualifier
 
xml-id: C18.S28.E9.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11713 / rank
 
Normal rank
Property / Symbols used: Q11713 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qmultiPochhammersym{\NVar{a_{1},a_{2},\dots,a_{r}}}{\NVar{q}}{\NVar{n}}}

\qmultiPochhammersym{\NVar{a_{1},a_{2},\dots,a_{r}}}{\NVar{q}}{\NVar{n}}
Property / Symbols used: Q11713 / qualifier
 
xml-id: C17.S2.SS1.p1.m6aedec
Property / Symbols used
 
Property / Symbols used: Q11743 / rank
 
Normal rank
Property / Symbols used: Q11743 / qualifier
 
Defining formula:

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

y
Property / Symbols used: Q11743 / qualifier
 
xml-id: C18.S1.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q11728 / rank
 
Normal rank
Property / Symbols used: Q11728 / qualifier
 
Defining formula:

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

q
Property / Symbols used: Q11728 / qualifier
 
xml-id: C18.S1.XMD3.m1gdec
Property / Symbols used
 
Property / Symbols used: Q11730 / rank
 
Normal rank
Property / Symbols used: Q11730 / qualifier
 
Defining formula:

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

m
Property / Symbols used: Q11730 / qualifier
 
xml-id: C18.S1.XMD5.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

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

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1gdec

Latest revision as of 12:22, 2 January 2020

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DLMF:18.28.E10
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{y=0}^{\infty}\frac{(1-q^{2y}a^{-2})\qmultiPochhammersym{a^{-2},(ab)^{-1}}{q}{y}}{(1-a^{-2})\qmultiPochhammersym{q,bqa^{-1}}{q}{y}}(ba^{-1})^{y}q^{y^{2}}\*\qinvAlSalamChiharapolyQ{n}@{\tfrac{1}{2}(aq^{-y}+a^{-1}q^{y})}{a}{b}{q^{-1}}\*\qinvAlSalamChiharapolyQ{m}@{\tfrac{1}{2}(aq^{-y}+a^{-1}q^{y})}{a}{b}{q^{-1}}=\frac{\qPochhammer{qa^{-2}}{q}{\infty}}{\qPochhammer{ba^{-1}q}{q}{\infty}}\qmultiPochhammersym{q,(ab)^{-1}}{q}{n}(ab)^{n}q^{-n^{2}}\Kroneckerdelta{n}{m}.}
    0 references
    DLMF id
    DLMF:18.28.E10
    0 references
    Symbols used
    Q10768
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Kroneckerdelta{\NVar{j}}{\NVar{k}}}
    xml-id
    introduction.Sx4.p1.t1.r4.m5acdec
    0 references
    Q11298
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{\NVar{a}}{\NVar{q}}{\NVar{n}}}
    xml-id
    C17.S2.SS1.p1.m2agdec
    0 references
    $$q^{-1}$$ -Al-Salam–Chihara polynomial
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qinvAlSalamChiharapolyQ{\NVar{n}}@{\NVar{x}}{\NVar{a}}{\NVar{b}}{\NVar{q}^{-1}}}
    xml-id
    C18.S28.E9.m2aadec
    0 references
    Q11713
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qmultiPochhammersym{\NVar{a_{1},a_{2},\dots,a_{r}}}{\NVar{q}}{\NVar{n}}}
    xml-id
    C17.S2.SS1.p1.m6aedec
    0 references
    Q11743
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y}
    xml-id
    C18.S1.XMD1.m1adec
    0 references
    Q11728
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q}
    xml-id
    C18.S1.XMD3.m1gdec
    0 references
    Q11730
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m}
    xml-id
    C18.S1.XMD5.m1cdec
    0 references
    Q11726
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n}
    xml-id
    C18.S1.XMD6.m1gdec
    0 references
     
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