DLMF:25.11.E19 (Q7693): Difference between revisions
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Changed an Item: Add constraint |
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 a>0}a>0 | |||
Property / constraint: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a>0} / rank | |||
Normal rank | |||
Property / Symbols used | |||
Property / Symbols used: Q11109 / rank | |||
Normal rank | |||
Property / Symbols used: Q11109 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BernoullinumberB{\NVar{n}}}\BernoullinumberB{\NVar{n}} | |||
Property / Symbols used: Q11109 / qualifier | |||
xml-id: C24.S2.SS1.m1abdec | |||
Property / Symbols used | |||
Property / Symbols used: Hurwitz zeta function / rank | |||
Normal rank | |||
Property / Symbols used: Hurwitz zeta function / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Hurwitzzeta@{\NVar{s}}{\NVar{a}}}\Hurwitzzeta@{\NVar{s}}{\NVar{a}} | |||
Property / Symbols used: Hurwitz zeta function / qualifier | |||
xml-id: C25.S11.E1.m2atdec | |||
Property / Symbols used | |||
Property / Symbols used: Q10770 / rank | |||
Normal rank | |||
Property / Symbols used: Q10770 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \diff{\NVar{x}}}\diff{\NVar{x}} | |||
Property / Symbols used: Q10770 / qualifier | |||
xml-id: C1.S4.SS4.m1acdec | |||
Property / Symbols used | |||
Property / Symbols used: Q10771 / rank | |||
Normal rank | |||
Property / Symbols used: Q10771 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int}\int | |||
Property / Symbols used: Q10771 / qualifier | |||
xml-id: C1.S4.SS4.m3acdec | |||
Property / Symbols used | |||
Property / Symbols used: principal branch of logarithm function / rank | |||
Normal rank | |||
Property / Symbols used: principal branch of logarithm function / qualifier | |||
Defining formula: 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.m2aadec | |||
Property / Symbols used | |||
Property / Symbols used: Q11110 / rank | |||
Normal rank | |||
Property / Symbols used: Q11110 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \perBernoulliB{\NVar{n}}@{\NVar{x}}}\perBernoulliB{\NVar{n}}@{\NVar{x}} | |||
Property / Symbols used: Q11110 / qualifier | |||
xml-id: C24.S2.SS3.m1abdec | |||
Property / Symbols used | |||
Property / Symbols used: Q10811 / rank | |||
Normal rank | |||
Property / Symbols used: Q10811 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@}\realpart@@ | |||
Property / Symbols used: Q10811 / qualifier | |||
xml-id: C1.S9.E2.m1agdec | |||
Property / Symbols used | |||
Property / Symbols used: Q12152 / rank | |||
Normal rank | |||
Property / Symbols used: Q12152 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x}x | |||
Property / Symbols used: Q12152 / qualifier | |||
xml-id: C25.S1.XMD5.m1edec | |||
Property / Symbols used | |||
Property / Symbols used: Q12161 / rank | |||
Normal rank | |||
Property / Symbols used: Q12161 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a}a | |||
Property / Symbols used: Q12161 / qualifier | |||
xml-id: C25.S1.XMD6.m1qdec | |||
Property / Symbols used | |||
Property / Symbols used: Q12149 / rank | |||
Normal rank | |||
Property / Symbols used: Q12149 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s}s | |||
Property / Symbols used: Q12149 / qualifier | |||
xml-id: C25.S1.XMD7.m1ndec | |||
Property / Symbols used | |||
Property / Symbols used: Q12162 / rank | |||
Normal rank | |||
Property / Symbols used: Q12162 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k}k | |||
Property / Symbols used: Q12162 / qualifier | |||
xml-id: C25.S11.XMD2.m1dec |
Latest revision as of 13:39, 2 January 2020
No description defined
Language | Label | Description | Also known as |
---|---|---|---|
English | DLMF:25.11.E19 |
No description defined |
Statements
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Hurwitzzeta'@{s}{a}=-\frac{\ln@@{a}}{a^{s}}\left(\frac{1}{2}+\frac{a}{s-1}\right)-\frac{a^{1-s}}{(s-1)^{2}}+\frac{s(s+1)}{2}\int_{0}^{\infty}\frac{(\perBernoulliB{2}@{x}-\BernoullinumberB{2})\ln@{x+a}}{(x+a)^{s+2}}\diff{x}-\frac{(2s+1)}{2}\int_{0}^{\infty}\frac{\perBernoulliB{2}@{x}-\BernoullinumberB{2}}{(x+a)^{s+2}}\diff{x},}
0 references
DLMF:25.11.E19
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{s}>-1}
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s\neq 1}
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a>0}
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BernoullinumberB{\NVar{n}}}
C24.S2.SS1.m1abdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Hurwitzzeta@{\NVar{s}}{\NVar{a}}}
C25.S11.E1.m2atdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \diff{\NVar{x}}}
C1.S4.SS4.m1acdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int}
C1.S4.SS4.m3acdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{\NVar{z}}}
C4.S2.E2.m2aadec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \perBernoulliB{\NVar{n}}@{\NVar{x}}}
C24.S2.SS3.m1abdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@}
C1.S9.E2.m1agdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x}
C25.S1.XMD5.m1edec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a}
C25.S1.XMD6.m1qdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s}
C25.S1.XMD7.m1ndec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k}
C25.S11.XMD2.m1dec
0 references