DLMF:10.22.E72 (Q3446): 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: Bessel function of the first kind / rank | |||
Normal rank | |||
Property / Symbols used: Bessel function of the first kind / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\NVar{\nu}}@{\NVar{z}}}\BesselJ{\NVar{\nu}}@{\NVar{z}} | |||
Property / Symbols used: Bessel function of the first kind / qualifier | |||
xml-id: C10.S2.E2.m2abedec | |||
Property / Symbols used | |||
Property / Symbols used: Q11470 / rank | |||
Normal rank | |||
Property / Symbols used: Q11470 / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \assLegendreQ[\NVar{\mu}]{\NVar{\nu}}@{\NVar{z}}}\assLegendreQ[\NVar{\mu}]{\NVar{\nu}}@{\NVar{z}} | |||
Property / Symbols used: Q11470 / qualifier | |||
xml-id: C14.S21.SS1.p1.m2adec | |||
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.m2aaddec | |||
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.m2aodec | |||
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.m1absdec | |||
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.m2agdec | |||
Property / Symbols used | |||
Property / Symbols used: hyperbolic cosine function / rank | |||
Normal rank | |||
Property / Symbols used: hyperbolic cosine function / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{\NVar{z}}}\cosh@@{\NVar{z}} | |||
Property / Symbols used: hyperbolic cosine function / qualifier | |||
xml-id: C4.S28.E2.m2aadec | |||
Property / Symbols used | |||
Property / Symbols used: hyperbolic sine function / rank | |||
Normal rank | |||
Property / Symbols used: hyperbolic sine function / qualifier | |||
Defining formula: Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh@@{\NVar{z}}}\sinh@@{\NVar{z}} | |||
Property / Symbols used: hyperbolic sine function / qualifier | |||
xml-id: C4.S28.E1.m2aadec | |||
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.m2agdec | |||
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.m3absdec | |||
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.m1aasdec | |||
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.m2aodec | |||
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.m1axdec |
Latest revision as of 13:28, 2 January 2020
No description defined
Language | Label | Description | Also known as |
---|---|---|---|
English | DLMF:10.22.E72 |
No description defined |
Statements
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\BesselJ{\mu}@{at}\BesselJ{\nu}@{bt}\BesselJ{\nu}@{ct}t^{1-\mu}\diff{t}=\frac{(bc)^{\mu-1}\sin@{(\mu-\nu)\cpi}(\sinh@@{\chi})^{\mu-\frac{1}{2}}}{(\frac{1}{2}\pi^{3})^{\frac{1}{2}}a^{\mu}}\expe^{(\mu-\frac{1}{2})\iunit\cpi}\assLegendreQ[\frac{1}{2}-\mu]{\nu-\frac{1}{2}}@{\cosh@@{\chi}},}
0 references
DLMF:10.22.E72
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{\mu}>-\tfrac{1}{2},\realpart@@{\nu}>-1,a>b+c,\cosh@@{\chi}=(a^{2}-b^{2}-c^{2})/(2bc)}
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\NVar{\nu}}@{\NVar{z}}}
C10.S2.E2.m2abedec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \assLegendreQ[\NVar{\mu}]{\NVar{\nu}}@{\NVar{z}}}
C14.S21.SS1.p1.m2adec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cpi}
C3.S12.E1.m2aaddec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\NVar{z}}}
C4.S14.E2.m2aodec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \diff{\NVar{x}}}
C1.S4.SS4.m1absdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expe}
C4.S2.E11.m2agdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{\NVar{z}}}
C4.S28.E2.m2aadec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh@@{\NVar{z}}}
C4.S28.E1.m2aadec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \iunit}
C1.S9.E1.m2agdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int}
C1.S4.SS4.m3absdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@}
C1.S9.E2.m1aasdec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{\NVar{z}}}
C4.S14.E1.m2aodec
0 references
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \nu}
C10.S1.XMD7.m1axdec
0 references