DLMF:18.15.E1 (Q5691): Difference between revisions
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Changed an Item: Add constraint |
Changed an Item: Add constraint |
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| (6 intermediate revisions by the same user not shown) | |||
| Property / Symbols used | |||
| Property / Symbols used: Q10759 / rank | |||
Normal rank | |||
| Property / Symbols used: Q10759 / qualifier | |||
Defining formula: 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.m1adec | |||
| 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.m2adec | |||
| Property / Symbols used | |||
| Property / Symbols used: cosine function / rank | |||
Normal rank | |||
| Property / Symbols used: cosine function / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\NVar{z}}}\cos@@{\NVar{z}} | |||
| Property / Symbols used: cosine function / qualifier | |||
xml-id: C4.S14.E2.m2adec | |||
| Property / Symbols used | |||
| Property / Symbols used: sine function / rank | |||
Normal rank | |||
| Property / Symbols used: sine function / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{\NVar{z}}}\sin@@{\NVar{z}} | |||
| Property / Symbols used: sine function / qualifier | |||
xml-id: C4.S14.E1.m2adec | |||
| 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.m1dec | |||
| 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.m1dec | |||
| Property / Symbols used | |||
| Property / Symbols used: DLMF:18.15.E2 / rank | |||
Normal rank | |||
| Property / Symbols used: DLMF:18.15.E2 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{m}(\theta)}f_{m}(\theta) | |||
| Property / Symbols used: DLMF:18.15.E2 / qualifier | |||
xml-id: C18.S15.XMD1.m1dec | |||
Latest revision as of 15:36, 2 January 2020
No description defined
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | DLMF:18.15.E1 |
No description defined |
Statements
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\sin@@{\tfrac{1}{2}\theta}\right)^{\alpha+\frac{1}{2}}\left(\cos@@{\tfrac{1}{2}\theta}\right)^{\beta+\frac{1}{2}}\JacobipolyP{\alpha}{\beta}{n}@{\cos@@{\theta}}=\pi^{-1}2^{2n+\alpha+\beta+1}\EulerBeta@{n+\alpha+1}{n+\beta+1}\*\left(\sum_{m=0}^{M-1}\frac{f_{m}(\theta)}{2^{m}\Pochhammersym{2n+\alpha+\beta+2}{m}}+\bigO@{n^{-M}}\right),}
0 references
DLMF:18.15.E1
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \bigO@{\NVar{x}}}
C2.S1.E3.m2adec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerBeta@{\NVar{a}}{\NVar{b}}}
C5.S12.E1.m2adec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \JacobipolyP{\NVar{\alpha}}{\NVar{\beta}}{\NVar{n}}@{\NVar{x}}}
C18.S3.T1.t1.r2.m2adec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Pochhammersym{\NVar{a}}{\NVar{n}}}
C5.S2.SS3.m1adec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cpi}
C3.S12.E1.m2adec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\NVar{z}}}
C4.S14.E2.m2adec
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{\NVar{z}}}
C4.S14.E1.m2adec
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Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m}
C18.S1.XMD5.m1dec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n}
C18.S1.XMD6.m1dec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f_{m}(\theta)}
C18.S15.XMD1.m1dec
0 references