DLMF:10.32.E14 (Q3534): Difference between revisions
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Changed an Item: Add constraint |
Changed an Item: Add constraint |
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(12 intermediate revisions by the same user not shown) | |||
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.m2addec | |||
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.m2aldec | |||
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.m2ahdec | |||
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.m1amdec | |||
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.m2ahdec | |||
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.m2abdec | |||
Property / Symbols used | |||
Property / Symbols used: Q10818 / rank | |||
Normal rank | |||
Property / Symbols used: Q10818 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Integers}\Integers | |||
Property / Symbols used: Q10818 / qualifier | |||
xml-id: introduction.Sx4.p2.t1.r20.m2adec | |||
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.m3amdec | |||
Property / Symbols used | |||
Property / Symbols used: modified Bessel function of the second kind / rank | |||
Normal rank | |||
Property / Symbols used: modified Bessel function of the second kind / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\NVar{\nu}}@{\NVar{z}}}\modBesselK{\NVar{\nu}}@{\NVar{z}} | |||
Property / Symbols used: modified Bessel function of the second kind / qualifier | |||
xml-id: C10.S25.E3.m2ahdec | |||
Property / Symbols used | |||
Property / Symbols used: Q11245 / rank | |||
Normal rank | |||
Property / Symbols used: Q11245 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \notin}\notin | |||
Property / Symbols used: Q11245 / qualifier | |||
xml-id: introduction.Sx4.p1.t1.r11.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.m1agdec | |||
Property / Symbols used | |||
Property / Symbols used: Q11426 / rank | |||
Normal rank | |||
Property / Symbols used: Q11426 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z}z | |||
Property / Symbols used: Q11426 / qualifier | |||
xml-id: C10.S1.XMD6.m1kdec | |||
Property / Symbols used | |||
Property / Symbols used: Q11427 / rank | |||
Normal rank | |||
Property / Symbols used: Q11427 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu}\nu | |||
Property / Symbols used: Q11427 / qualifier | |||
xml-id: C10.S1.XMD7.m1idec |
Latest revision as of 13:44, 2 January 2020
No description defined
Language | Label | Description | Also known as |
---|---|---|---|
English | DLMF:10.32.E14 |
No description defined |
Statements
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\nu}@{z}=\frac{1}{2\pi^{2}i}\left(\frac{\pi}{2z}\right)^{\frac{1}{2}}e^{-z}\cos@{\nu\pi}\*\int_{-i\infty}^{i\infty}\EulerGamma@{t}\EulerGamma@{\tfrac{1}{2}-t-\nu}\EulerGamma@{\tfrac{1}{2}-t+\nu}(2z)^{t}\diff{t},}
0 references
DLMF:10.32.E14
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu-\tfrac{1}{2}\notin\Integers,|\phase@@{z}|<\tfrac{3}{2}\pi}
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{\NVar{z}}}
C5.S2.E1.m2addec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cpi}
C3.S12.E1.m2aldec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\NVar{z}}}
C4.S14.E2.m2ahdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \diff{\NVar{x}}}
C1.S4.SS4.m1amdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expe}
C4.S2.E11.m2ahdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \iunit}
C1.S9.E1.m2abdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Integers}
introduction.Sx4.p2.t1.r20.m2adec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int}
C1.S4.SS4.m3amdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \modBesselK{\NVar{\nu}}@{\NVar{z}}}
C10.S25.E3.m2ahdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \notin}
introduction.Sx4.p1.t1.r11.m2adec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phase}
C1.S9.E7.m1agdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z}
C10.S1.XMD6.m1kdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu}
C10.S1.XMD7.m1idec
0 references