DLMF:18.15.E6 (Q5696): Difference between revisions

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‎Changed an Item: Add constraint
 
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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.m2abdec
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.m1ddec
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.m1ddec
Property / Symbols used
 
Property / Symbols used: DLMF:18.15.E5 / rank
 
Normal rank
Property / Symbols used: DLMF:18.15.E5 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho}

\rho
Property / Symbols used: DLMF:18.15.E5 / qualifier
 
xml-id: C18.S15.XMD4.m1adec
Property / Symbols used
 
Property / Symbols used: DLMF:18.15.E7 / rank
 
Normal rank
Property / Symbols used: DLMF:18.15.E7 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \varepsilon_{M}(\rho,\theta)}

\varepsilon_{M}(\rho,\theta)
Property / Symbols used: DLMF:18.15.E7 / qualifier
 
xml-id: C18.S15.XMD5.m1dec
Property / Symbols used
 
Property / Symbols used: Q11752 / rank
 
Normal rank
Property / Symbols used: Q11752 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{m}(\theta)}

A_{m}(\theta)
Property / Symbols used: Q11752 / qualifier
 
xml-id: C18.S15.XMD6.m1dec
Property / Symbols used
 
Property / Symbols used: Q11753 / rank
 
Normal rank
Property / Symbols used: Q11753 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{m}(\theta)}

B_{m}(\theta)
Property / Symbols used: Q11753 / qualifier
 
xml-id: C18.S15.XMD7.m1dec

Latest revision as of 15:37, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:18.15.E6
No description defined

    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\sin@@{\tfrac{1}{2}\theta})^{\alpha+\frac{1}{2}}(\cos@@{\tfrac{1}{2}\theta})^{\beta+\frac{1}{2}}\JacobipolyP{\alpha}{\beta}{n}@{\cos@@{\theta}}=\frac{\EulerGamma@{n+\alpha+1}}{2^{\frac{1}{2}}\rho^{\alpha}n!}\*\left(\theta^{\frac{1}{2}}\BesselJ{\alpha}@{\rho\theta}\sum_{m=0}^{M}\dfrac{A_{m}(\theta)}{\rho^{2m}}+\theta^{\frac{3}{2}}\BesselJ{\alpha+1}@{\rho\theta}\sum_{m=0}^{M-1}\dfrac{B_{m}(\theta)}{\rho^{2m+1}}+\varepsilon_{M}(\rho,\theta)\right),}
    0 references
    DLMF id
    DLMF:18.15.E6
    0 references
    Symbols used
    Bessel function of the first kind
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \BesselJ{\NVar{\nu}}@{\NVar{z}}}
    xml-id
    C10.S2.E2.m2adec
    0 references
    gamma function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \EulerGamma@{\NVar{z}}}
    xml-id
    C5.S2.E1.m2adec
    0 references
    Q11660
    Defining formula
    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}}}
    xml-id
    C18.S3.T1.t1.r2.m2aadec
    0 references
    cosine function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
    0 references
    Q10755
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle !}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    sine function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{\NVar{z}}}
    xml-id
    C4.S14.E1.m2abdec
    0 references
    Q11730
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m}
    xml-id
    C18.S1.XMD5.m1ddec
    0 references
    Q11726
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n}
    xml-id
    C18.S1.XMD6.m1ddec
    0 references
    DLMF:18.15.E5
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho}
    xml-id
    C18.S15.XMD4.m1adec
    0 references
    DLMF:18.15.E7
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \varepsilon_{M}(\rho,\theta)}
    xml-id
    C18.S15.XMD5.m1dec
    0 references
    Q11752
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{m}(\theta)}
    xml-id
    C18.S15.XMD6.m1dec
    0 references
    Q11753
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{m}(\theta)}
    xml-id
    C18.S15.XMD7.m1dec
    0 references
     
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