DLMF:30.11.E6 (Q8901): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q10901 / rank
 
Normal rank
Property / Symbols used: Q10901 / qualifier
 
Defining formula:

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

\imagpart@@
Property / Symbols used: Q10901 / qualifier
 
xml-id: C1.S9.E2.m2adec
Property / Symbols used
 
Property / Symbols used: radial spheroidal wave function / rank
 
Normal rank
Property / Symbols used: radial spheroidal wave function / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \radsphwaveS{\NVar{m}}{\NVar{j}}{\NVar{n}}@{\NVar{z}}{\NVar{\gamma}}}

\radsphwaveS{\NVar{m}}{\NVar{j}}{\NVar{n}}@{\NVar{z}}{\NVar{\gamma}}
Property / Symbols used: radial spheroidal wave function / qualifier
 
xml-id: C30.S11.E3.m2afdec
Property / Symbols used
 
Property / Symbols used: Q12401 / rank
 
Normal rank
Property / Symbols used: Q12401 / qualifier
 
Defining formula:

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

z
Property / Symbols used: Q12401 / qualifier
 
xml-id: C30.S1.XMD1.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12408 / rank
 
Normal rank
Property / Symbols used: Q12408 / qualifier
 
Defining formula:

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

m
Property / Symbols used: Q12408 / qualifier
 
xml-id: C30.S1.XMD4.m1cdec
Property / Symbols used
 
Property / Symbols used: Q12409 / rank
 
Normal rank
Property / Symbols used: Q12409 / qualifier
 
Defining formula:

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

n\geq m
Property / Symbols used: Q12409 / qualifier
 
xml-id: C30.S1.XMD5.m1gdec
Property / Symbols used
 
Property / Symbols used: spherical function (locally) / rank
 
Normal rank
Property / Symbols used: spherical function (locally) / qualifier
 
Defining formula:

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

\psi_{k}^{(j)}(z)
Property / Symbols used: spherical function (locally) / qualifier
 
xml-id: C30.S11.XMD3.m1bdec
Property / Symbols used
 
Property / Symbols used: Q12404 / rank
 
Normal rank
Property / Symbols used: Q12404 / qualifier
 
Defining formula:

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma^{2}}

\gamma^{2}
Property / Symbols used: Q12404 / qualifier
 
xml-id: C30.S2.XMD3.m1cdec

Latest revision as of 01:48, 2 January 2020

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DLMF:30.11.E6
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    Statements

    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \radsphwaveS{m}{j}{n}@{z}{\gamma}=\begin{cases}\psi_{n}^{(j)}(\gamma z)+\bigO@{z^{-2}e^{|\imagpart@@{z}|}},&j=1,2,\\ \psi_{n}^{(j)}(\gamma z)\left(1+\bigO@{z^{-1}}\right),&j=3,4.\end{cases}}
    0 references
    DLMF id
    DLMF:30.11.E6
    0 references
    Symbols used
    order not exceeding
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \bigO@{\NVar{x}}}
    xml-id
    C2.S1.E3.m2adec
    0 references
    base of natural logarithm
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expe}
    xml-id
    C4.S2.E11.m2adec
    0 references
    Q10901
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \imagpart@@}
    xml-id
    C1.S9.E2.m2adec
    0 references
    radial spheroidal wave function
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \radsphwaveS{\NVar{m}}{\NVar{j}}{\NVar{n}}@{\NVar{z}}{\NVar{\gamma}}}
    xml-id
    C30.S11.E3.m2afdec
    0 references
    Q12401
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z}
    xml-id
    C30.S1.XMD1.m1cdec
    0 references
    Q12408
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m}
    xml-id
    C30.S1.XMD4.m1cdec
    0 references
    Q12409
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n\geq m}
    xml-id
    C30.S1.XMD5.m1gdec
    0 references
    spherical function (locally)
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \psi_{k}^{(j)}(z)}
    xml-id
    C30.S11.XMD3.m1bdec
    0 references
    Q12404
    Defining formula
    Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma^{2}}
    xml-id
    C30.S2.XMD3.m1cdec
    0 references
     
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