DLMF:15.8.E32 (Q5089): 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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(11 intermediate revisions by the same user not shown) | |||
Property / constraint | |||
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\phase@{-z}|<\frac{1}{3}\pi}|\phase@{-z}|<\frac{1}{3}\pi | |||
Property / constraint: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\phase@{-z}|<\frac{1}{3}\pi} / rank | |||
Normal rank | |||
Property / constraint | |||
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |z|>1}|z|>1 | |||
Property / constraint: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |z|>1} / rank | |||
Normal rank | |||
Property / constraint | |||
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\operatorname{ph}\left(-z\right)|<\frac{1}{3}\pi}|\operatorname{ph}\left(-z\right)|<\frac{1}{3}\pi | |||
Property / constraint: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\operatorname{ph}\left(-z\right)|<\frac{1}{3}\pi} / rank | |||
Normal rank | |||
Property / Symbols used | |||
Property / Symbols used: gamma function / rank | |||
Normal rank | |||
Property / Symbols used: gamma function / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{\NVar{z}}}\EulerGamma@{\NVar{z}} | |||
Property / Symbols used: gamma function / qualifier | |||
xml-id: C5.S2.E1.m2amdec | |||
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 | |||
Defining formula: 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.m2audec | |||
Property / Symbols used | |||
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank | |||
Normal rank | |||
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cpi}\cpi | |||
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier | |||
xml-id: C3.S12.E1.m2asdec | |||
Property / Symbols used | |||
Property / Symbols used: base of natural logarithm / rank | |||
Normal rank | |||
Property / Symbols used: base of natural logarithm / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expe}\expe | |||
Property / Symbols used: base of natural logarithm / qualifier | |||
xml-id: C4.S2.E11.m2adec | |||
Property / Symbols used | |||
Property / Symbols used: imaginary unit / rank | |||
Normal rank | |||
Property / Symbols used: imaginary unit / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \iunit}\iunit | |||
Property / Symbols used: imaginary unit / qualifier | |||
xml-id: C1.S9.E1.m2adec | |||
Property / Symbols used | |||
Property / Symbols used: Q10817 / rank | |||
Normal rank | |||
Property / Symbols used: Q10817 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase}\phase | |||
Property / Symbols used: Q10817 / qualifier | |||
xml-id: C1.S9.E7.m1asdec | |||
Property / Symbols used | |||
Property / Symbols used: Q11644 / rank | |||
Normal rank | |||
Property / Symbols used: Q11644 / qualifier | |||
Defining formula: 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.m1aedec | |||
Property / Symbols used | |||
Property / Symbols used: Q11645 / rank | |||
Normal rank | |||
Property / Symbols used: Q11645 / qualifier | |||
Defining formula: 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.m1addec | |||
Property / Symbols used | |||
Property / Symbols used: Q11659 / rank | |||
Normal rank | |||
Property / Symbols used: Q11659 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta}\zeta | |||
Property / Symbols used: Q11659 / qualifier | |||
xml-id: C15.S8.XMD1.m1dec |
Latest revision as of 14:07, 2 January 2020
No description defined
Language | Label | Description | Also known as |
---|---|---|---|
English | DLMF:15.8.E32 |
No description defined |
Statements
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\left(1-z^{3}\right)^{a}}{\left(-z\right)^{3a}}\left(\frac{1}{\EulerGamma@{a+\frac{2}{3}}\EulerGamma@{\frac{2}{3}}}\hyperF@@{a}{a+\frac{1}{3}}{\frac{2}{3}}{z^{-3}}+\frac{e^{\frac{1}{3}\pi\iunit}}{z\EulerGamma@{a}\EulerGamma@{\frac{4}{3}}}\hyperF@@{a+\frac{1}{3}}{a+\frac{2}{3}}{\frac{4}{3}}{z^{-3}}\right)=\frac{3^{\frac{3}{2}a+\frac{1}{2}}e^{\frac{1}{2}a\pi\iunit}\EulerGamma@{a+\frac{1}{3}}(1-\zeta)^{a}}{2\pi\EulerGamma@{2a+\frac{2}{3}}(-\zeta)^{2a}}\hyperF@@{a+\frac{1}{3}}{3a}{2a+\frac{2}{3}}{\zeta^{-1}},}
0 references
DLMF:15.8.E32
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\phase@{-z}|<\frac{1}{3}\pi}
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |z|>1}
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle |\operatorname{ph}\left(-z\right)|<\frac{1}{3}\pi}
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{\NVar{z}}}
C5.S2.E1.m2amdec
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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}}}
C15.S2.E1.m2audec
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cpi}
C3.S12.E1.m2asdec
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expe}
C4.S2.E11.m2adec
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \iunit}
C1.S9.E1.m2adec
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase}
C1.S9.E7.m1asdec
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z}
C15.S1.XMD3.m1aedec
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a}
C15.S1.XMD4.m1addec
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta}
C15.S8.XMD1.m1dec
0 references