DLMF:25.11.E20 (Q7694): Difference between revisions
Jump to navigation
Jump to search
Changed an Item: Add constraint |
Changed an Item: Add constraint |
||
(4 intermediate revisions by the same user not shown) | |||
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.m1ahdec | |||
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.m1fdec | |||
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.m1rdec | |||
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.m1odec | |||
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.m1adec |
Latest revision as of 13:40, 2 January 2020
No description defined
Language | Label | Description | Also known as |
---|---|---|---|
English | DLMF:25.11.E20 |
No description defined |
Statements
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (-1)^{k}\Hurwitzzeta^{(k)}@{s}{a}=\frac{(\ln@@{a})^{k}}{a^{s}}\left(\frac{1}{2}+\frac{a}{s-1}\right)+k!a^{1-s}\sum_{r=0}^{k-1}\frac{(\ln@@{a})^{r}}{r!(s-1)^{k-r+1}}-\frac{s(s+1)}{2}\int_{0}^{\infty}\frac{(\perBernoulliB{2}@{x}-\BernoullinumberB{2})(\ln@{x+a})^{k}}{(x+a)^{s+2}}\diff{x}+\frac{k(2s+1)}{2}\int_{0}^{\infty}\frac{(\perBernoulliB{2}@{x}-\BernoullinumberB{2})(\ln@{x+a})^{k-1}}{(x+a)^{s+2}}\diff{x}-\frac{k(k-1)}{2}\int_{0}^{\infty}\frac{(\perBernoulliB{2}@{x}-\BernoullinumberB{2})(\ln@{x+a})^{k-2}}{(x+a)^{s+2}}\diff{x},}
0 references
DLMF:25.11.E20
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.m1acdec
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.m2audec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \diff{\NVar{x}}}
C1.S4.SS4.m1addec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle !}
introduction.Sx4.p1.t1.r15.m5abdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int}
C1.S4.SS4.m3addec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{\NVar{z}}}
C4.S2.E2.m2abdec
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.m1acdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@}
C1.S9.E2.m1ahdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x}
C25.S1.XMD5.m1fdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a}
C25.S1.XMD6.m1rdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s}
C25.S1.XMD7.m1odec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k}
C25.S11.XMD2.m1adec
0 references