DLMF:17.2.E42 (Q5332): Difference between revisions
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Created a new Item: Wikidata Toolkit example test item creation |
Changed an Item: Add constraint |
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(8 intermediate revisions by the same user not shown) | |||
Property / Symbols used | |||
Property / Symbols used: Q10754 / rank | |||
Normal rank | |||
Property / Symbols used: Q10754 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{\NVar{m}}{\NVar{n}}}\binom{\NVar{m}}{\NVar{n}} | |||
Property / Symbols used: Q10754 / qualifier | |||
xml-id: C1.S2.SS1.m1amdec | |||
Property / Symbols used | |||
Property / Symbols used: Q10755 / rank | |||
Normal rank | |||
Property / Symbols used: Q10755 / qualifier | |||
Defining formula: 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.m5aadec | |||
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.m2aaidec | |||
Property / Symbols used | |||
Property / Symbols used: $$q$$ -binomial coefficient (or Gaussian polynomial) / rank | |||
Normal rank | |||
Property / Symbols used: $$q$$ -binomial coefficient (or Gaussian polynomial) / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qbinom{\NVar{n}}{\NVar{m}}{\NVar{q}}}\qbinom{\NVar{n}}{\NVar{m}}{\NVar{q}} | |||
Property / Symbols used: $$q$$ -binomial coefficient (or Gaussian polynomial) / qualifier | |||
xml-id: C17.S2.E27.m2aldec | |||
Property / Symbols used | |||
Property / Symbols used: Q11710 / rank | |||
Normal rank | |||
Property / Symbols used: Q11710 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q}q | |||
Property / Symbols used: Q11710 / qualifier | |||
xml-id: C17.S1.XMD10.m1andec | |||
Property / Symbols used | |||
Property / Symbols used: Q11712 / rank | |||
Normal rank | |||
Property / Symbols used: Q11712 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle j}j | |||
Property / Symbols used: Q11712 / qualifier | |||
xml-id: C17.S1.XMD2.m1idec | |||
Property / Symbols used | |||
Property / Symbols used: Q11711 / rank | |||
Normal rank | |||
Property / Symbols used: Q11711 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n}n | |||
Property / Symbols used: Q11711 / qualifier | |||
xml-id: C17.S1.XMD4.m1akdec | |||
Property / Symbols used | |||
Property / Symbols used: Q11718 / rank | |||
Normal rank | |||
Property / Symbols used: Q11718 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z}z | |||
Property / Symbols used: Q11718 / qualifier | |||
xml-id: C17.S1.XMD7.m1edec | |||
Property / Symbols used | |||
Property / Symbols used: $$q$$ -differential operator (locally) / rank | |||
Normal rank | |||
Property / Symbols used: $$q$$ -differential operator (locally) / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathcal{D}_{q}}\mathcal{D}_{q} | |||
Property / Symbols used: $$q$$ -differential operator (locally) / qualifier | |||
xml-id: C17.S2.XMD1.m1adec |
Latest revision as of 14:51, 2 January 2020
No description defined
Language | Label | Description | Also known as |
---|---|---|---|
English | DLMF:17.2.E42 |
No description defined |
Statements
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f^{[n]}(z)=\mathcal{D}_{q}^{n}f(z)=\begin{cases}z^{-n}(1-q)^{-n}\sum_{j=0}^{n}q^{-nj+\binom{j+1}{2}}(-1)^{j}\qbinom{n}{j}{q}f(zq^{j}),&z\neq 0,\\ \dfrac{f^{(n)}(0)\qPochhammer{q}{q}{n}}{n!(1-q)^{n}},&z=0.\end{cases}}
0 references
DLMF:17.2.E42
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{\NVar{m}}{\NVar{n}}}
C1.S2.SS1.m1amdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle !}
introduction.Sx4.p1.t1.r15.m5aadec
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{\NVar{a}}{\NVar{q}}{\NVar{n}}}
C17.S2.SS1.p1.m2aaidec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qbinom{\NVar{n}}{\NVar{m}}{\NVar{q}}}
C17.S2.E27.m2aldec
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q}
C17.S1.XMD10.m1andec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle j}
C17.S1.XMD2.m1idec
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n}
C17.S1.XMD4.m1akdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z}
C17.S1.XMD7.m1edec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathcal{D}_{q}}
C17.S2.XMD1.m1adec
0 references